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.

3. LAHALLHL
FOR RIGHT TRIANGLES ONLY
AASASASASSSS
FOR ALL TRIANGLES

4. 30°
30°
Q1. Why aren’t these triangles congruent?
What do we call these triangles?
So, how do we prove that triangles are
congruent?

5. 1. A   D
2. AB  DE
3.  B   E
ABC   DEF
C

6. 1. A  D
2. B  E
3. BC  EF
ABC   DEF

7. 1. AB  DE
2. BC  EF
3. AC  DF
ABC   DEF

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