Two geometrical figures are similar if one can be obtained from the other by a uniform scaling (enlarging or shrinking) while maintaining the same shape. Specifically, two polygons are similar if they have the same corresponding angles and proportional side lengths, and two triangles are similar if they have the same three angles. The similarity of figures is denoted with a tilde symbol such as ΔABC ~ ΔDEF for similar triangles.

2. SIMILARITY OF FIGURES
 Two geometrical objects are called similar
if one is the result of a uniform scaling
(enlarging or shrinking) of the other.

3. SIMILARITY OF FIGURES
 Two geometrical objects are called similar
if one is the result of a uniform scaling
(enlarging or shrinking) of the other.
 One can be obtained from the other by
uniformly "stretching", possibly with
additional rotation

4. SIMILARITY OF FIGURES
 Bothhave the same shape, or additionally
the other is mirror image of the first i.e.,
one has the same shape as the mirror
image of the other .

5. SIMILARITY OF FIGURES
Example
 All circles are similar to each other.

6. SIMILARITY OF FIGURES
Example
 All circles are similar to each other.

7. SIMILARITY OF FIGURES
Example
 All circles are similar to each other.

8. SIMILARITY OF FIGURES
Example
 All lines are similar to each other.

9. SIMILARITY OF FIGURES
Example
 All lines are similar to each other.

10. SIMILARITY OF FIGURES
Example
 All lines are similar to each other.

11. SIMILARITY OF FIGURES
Example
 All lines are similar to each other.

12. SIMILARITY OF FIGURES
Example
 All squares are similar to each other.

13. SIMILARITY OF FIGURES
Example
 All squares are similar to each other.

14. SIMILARITY OF FIGURES
Example
 All squares are similar to each other.

15. SIMILARITY OF FIGURES
Example
 All squares are similar to each other.

16. SIMILARITY OF FIGURES
Example
 All parabolas are similar to each other.

17. SIMILARITY OF FIGURES
Example
 But all ellipses are not all similar to each
other,

18. SIMILARITY OF FIGURES

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100. SIMILARITY OF FIGURES

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157. SIMILARITY OF FIGURES

158. SIMILARITY OF FIGURES

159. SIMILARITY OF FIGURES

160. SIMILARITY OF FIGURES

161. SIMILARITY OF FIGURES

162. SIMILARITY OF FIGURES

163. SIMILARITY OF FIGURES
SIMILARITY THROUGH MIRROR IMAGE

164. SIMILARITY OF FIGURES
SIMILARITY THROUGH MIRROR IMAGE

165. SIMILARITY OF FIGURES
SIMILARITY THROUGH MIRROR IMAGE

166. SIMILARITY OF FIGURES
SIMILARITY THROUGH MIRROR IMAGE

167. SIMILARITY OF POLYGONS

168. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.

169. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.

170. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
A

171. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
A
B

172. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
A
B C

173. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
A D
B C

174. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
A D
B C

175. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
A D
B C

176. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
A D
P
B C

177. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
A D
P
C Q
B

178. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
A D
P
C Q R
B

179. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
A D
P S
C Q R
B

180. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
T
A D
P S
C Q R
B

181. SIMILARITY OF POLYGONS
 Two polygons are similar if and only if they
have the same corresponding angles and
the lengths of their corresponding sides
are proportional.
 If two polygons ABCDE and PQRST are
similar, we write ABCDE ~PQRST.
E
T
A D
P S
C Q R
B

182. SIMILARITY OF TRIANGLES
 Twotriangles are similar if and only if they
have the same three angles.
 However, since the sum of the interior
angles in a triangle is fixed, as long as two
angles are the same, all three are same.

183. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

184. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

185. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

186. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

187. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

188. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

189. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

190. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

191. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

192. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

193. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

194. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

195. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

196. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

197. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

198. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

199. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

200. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

201. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

202. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

203. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

204. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

205. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

206. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

207. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

208. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

209. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

210. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

211. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

212. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

213. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

214. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

215. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

216. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

217. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

218. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

219. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

220. SIMILARITY OF TRIANGLES
 Iftriangle ABC is similar to triangle DEF,
then this relation can be denoted as ∆
ABC ~ ∆ DEF

221. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

222. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

223. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

224. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

225. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

226. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

227. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

228. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

229. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AAA-similarity): If in two triangles, the
corresponding angles are equal, then their
corresponding sides are proportional and
triangles are similar.

230. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

231. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

232. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

233. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

234. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

235. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

236. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (AA-similarity): If in two triangles, any two
corresponding angles are equal, then
triangles are similar.

237. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

238. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

239. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

240. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

241. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

242. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

243. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

244. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SAS-similarity): If in two triangles, any
two corresponding sides are proportional
and included angle are equal, then
triangles are similar.

245. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

246. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

247. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

248. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

249. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

250. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

251. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

252. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

253. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

254. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

255. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

256. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

257. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

258. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

259. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

260. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

261. SIMILARITY OF TRIANGLES
Rules for checking to similarity of two triangles.
 (SSS-similarity): If in two triangles, all
three corresponding sides of one are
proportional to corresponding sides of
other, then triangles are similar.

262. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.

263. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
 Thale’s Theorem:triangles.

264. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.

265. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.

266. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A

267. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
B

268. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
B C

269. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
B C

270. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
P
B C

271. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
P Q
B C

272. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
AP AQ
= P Q
PB QC C
B

273. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
AP AQ
= P Q
PB QC C
B

274. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Thale’s Theorem: If a line is drawn parallel
to one side of a triangle intersecting the other
two sides in distinct points then other two
sides are divided in the same ratio.
A
AP AQ
= P Q
PB QC C
B

275. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
 triangles.
Angle bisector result:

276. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.

277. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.

278. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A

279. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A
B

280. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A
B C

281. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A
B C

282. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A
Q
B C

283. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A
AB AQ
= Q
BC QC C
B

284. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 Angle bisector result: The bisector of an
angle in a triangle divides the opposite side
in the same ratio as ratio of sides containing
the angle.
A
AB AQ
= Q
BC QC C
B

285. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
 The area result: triangles.

286. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.

287. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.

288. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A

289. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
B

290. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
B C

291. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
B C

292. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
P
B C

293. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
P
B C Q

294. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
P
B C Q R

295. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
ar (∆ ABC ) AB 2
BC 2
AC 2 P
= = =
ar (∆ PQR) PQ QR
2 2
PR 2
B C Q R

296. SIMILARITY OF TRIANGLES
Other Rules related to similarity of two
triangles.
 The area result: The ratio of area of two
similar triangles is equal to the ratio of the
squares of their corresponding sides.
A
ar (∆ ABC ) AB 2
BC 2
AC 2 P
= = =
ar (∆ PQR) PQ QR
2 2
PR 2
B C Q R