The document discusses angle sum angle congruence and provides examples of using the Angle-Side-Angle (ASA) criterion to show triangle congruence. It includes: - An introduction to ASA congruency stating that two triangles are congruent if two angles and the included side of one triangle are equal to those of the other triangle. - Examples worked out by various group members applying ASA to show different triangles are congruent, find missing angle measures, and determine if side lengths are equal. - Questions with answers reviewing the concept that for ASA congruence, two angles and the included side must be equal between the two triangles.

1. Angle Sum Angle Congruence
Group Members:
Japneet Kaur (Roll No 26)
Arshia Narang (Roll No 27)
Agam Singh (Roll No 28)
Rhythm Kaur (Roll No 29)
Divyam Kabra (Roll No 30)
Arya Jain (Roll No 31)
Rubaani Kaur (Roll No 32)

2. ASA
CONGRUENCY
INTRODUCTION
Two triangles are congruent, if two angles
and the included side of one triangle are
respectively equal to the two angles and
the included side of the other triangle.
IN ABOVE GIVEN FIGURE, ANGLE C= ANGLE E ,
ANGLE B = ANGLE D AND SIDES BETWEEN ANGLE B
AND ANGLE C , ANGLE D AND ANGLE E ARE EQUAL
TO EACH OTHER i.e BC = DE . HENCE TRIANGLE
ABC IS CONGRUENT TO TRIANGLE DEF.
A
B C D
F
E
ARYA JAIN

3. In the adjacent figure, AD bisects A and AD ⊥ BC.
(i) Is ΔADB ≅ ΔADC?
(ii) State the three pairs of matching parts you have used in (i)
(iii) Is it true to say that BD = DC?
Solution:
(i) Yes, ΔADB≅ΔADC, by ASA criterion of congruency.
(ii) We have used :
∠BAD = ∠CAD (AD bisects <A)
∠ADB = ∠ADC = 90o (AD ⊥ BC)
and AD = DA
(iii) Yes, BD = DC since, ΔADB ≅ ΔADC
Japneet Kaur

4. In the given congruent triangles under ASA, find the value of x and y,
ΔPQR = ΔSTU
Given: ΔPQR ΔSTU (By ASA rule)
∠Q = ∠T = 60° (given)
QR¯ = TU¯ = 4 cm (given)
∠x = 30° (for ASA rule)
Now in ΔSTU,
∠S + ∠T + ∠U = 180° (Angle sum property)
∠y + 60° + ∠x = 180°
∠y + 60° + 30° = 180°
∠y + 90° = 180°
∠y = 180° – 90° = 90°
Hence, x = 30° and y = 90°
Arshia Narang

5. Q 1) We want to show that ∆ ART = ∆ PEN. We have to use
ASA criterion. We have AT = PN, ∠A = ∠P. What more we
need to show?
(a) ∠T = ∠N
(b) ∠T = ∠E
(c) ∠T = ∠P
(d) None of these
Q 2)
Answer: (a) ∠T = ∠N
Agam Singh

6. Ans
Agam Singh

7. Q1 In the given figure, ∆ARO ≅ ∆ __________
Solution:
PQO: In ∆ARO and ∆PQO,
∠ARO = ∠PQO = 55°
∠AOR = ∠POQ [Vertically opposite angles]
∴ ∠RAQ = ∠QPO
[∵ If two angles of a triangle are equal to two
angles of another triangle then third angle is
also equal]
AO = PO = 2.5 cm
∴ ∆ARO ≅ ∆PQO [ASA criterion]
Rhythm Kaur

8. Q1.) How are two triangles congruent ?
Two triangles are congruent when 2 angles and the remaining side
are equal to the other triangles 2 angles and the remaining side.
Q2.) Is triangle congruent to triangle ABC ?
Yes triangle ABC is congruent to
triangle XYZ as they have 2 equal
angles and the remaining side is
also equal.
A
B C
X
Y Z
D
E F
P
Q R
Is triangle PQR congruent to
triangle DEF ?
No triangle PQR is not congruent
to triangle DEF as they don’t have
2 equal sides and the remaining
side is also not equal
Divyam Kabra

9. Rubaani Kaur