The document discusses two pairs of similar triangles, ΔABC and ΔPQR, and ΔXYZ and ΔUVW. For the first pair, the angles of one triangle are equal to the corresponding angles of the other triangle. For the second pair, the ratios of the corresponding sides are equal, so the angles of the same size are also equal. The student is asked to identify reasons the triangles are similar by their corresponding parts and write proportional relationships between the sides.

1. Student’s Task11..33
Name:............................ Date: ............................
Similar Triangles
1. a. R
C
10
10
4
A
3
B P
8
Q
ΔABC and ΔPQR are similar because ………………………………….…
…………...................................................................................................
…………...................................................................................................
b. Z
W
80o 80o
70o
30o U V
X Y
ΔXYZ and ΔUVW are similar because ……………………………….…
…………...................................................................................................
…………...................................................................................................
2. a. ΔABC and ΔPQR are similar because
∠A = ∠R
∠B = ∠Q
∠C = ∠P
Therefore, the proportion of the corresponding sides is
........
=
.......
=
........
........ ........ .........
Mathematics for Junior High School Grade 9 / 5

2. b. ΔXYZ and ΔUVW are similar because
VW
=
UV
=
UW
.

3. XY XZ YZ
Therefore, the angles of the same size are
∠... = ∠...
∠... = ∠...
∠... = ∠...
6 / Student’s Worksheet – Similarity and Congruency