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Geometry the congruence of triangles
1.
2. Congruent Triangles
• Congruent triangles have
three congruent sides and
three congruent angles.
• However, triangles can be
proved congruent without
showing 3 pairs of
congruent sides and angles.
8. 1. AB DE
2. A D
3. AC DF
ABC DEF
F
9. If two isosceles triangles have a common line segments joining their
vertices bisects the common base at right angles.
Given Two
ABC and DBC with the same base BC, in which AB=AC and
DB=DC. Also ,AD meets BC in E.
To Prove- BE=CE and AEB= AEC=90*
A
B
C
D
E
1 2
3 4
B
A
CE
3 4
1 2
10. In ABD & ACD, we have :
AB=AC (given)
DB=DC(given)
AD=AD(common)
ABD= ACD(SSS criteria)
Now, in ABE & ACE, we have:
AB=AC (given) AE=AE(common)
ABE= ACE (SAS criteria ) BE=CE (.) & 3=4
But 3= 4=180*(linear pair)
24=180*,i.e.4=90*
3=4=90*
Hence, BE=CE & AEB =AEC=90*
B
D
A
CE
3 4
1 2
A
B C
D
E
1 2
3 4
THUS PROVED