Worksheet: Congruence of Triangles: ASA and AAS Criteria

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In this worksheet, we will practice identifying congruence in triangles using ASA and AAS criteria and finding a missing angle or side length.

Q1:

Determine the lengths of 𝐴 𝑁 and 𝐵 𝑁 .

  • A 𝐴 𝑁 = 3 7 c m , 𝐵 𝑁 = 2 2 c m
  • B 𝐴 𝑁 = 3 8 c m , 𝐵 𝑁 = 2 2 c m
  • C 𝐴 𝑁 = 3 7 c m , 𝐵 𝑁 = 2 1 c m
  • D 𝐴 𝑁 = 3 8 c m , 𝐵 𝑁 = 2 1 c m

Q2:

Which congruence criteria can be used to prove that the two triangles in the given figure are congruent?

  • A SAS
  • B SSS
  • C ASA

Q3:

Which congruence criteria can be used to prove that the two triangles in the given figure are congruent?

  • A SAS
  • B SSS
  • C ASA

Q4:

Find the lengths of 𝐶 𝐵 and 𝐴 𝐷 .

  • A 𝐶 𝐵 = 2 0 c m , 𝐴 𝐷 = 2 0 c m
  • B 𝐶 𝐵 = 1 2 c m , 𝐴 𝐷 = 2 0 c m
  • C 𝐶 𝐵 = 1 2 c m , 𝐴 𝐷 = 1 2 c m
  • D 𝐶 𝐵 = 2 0 c m , 𝐴 𝐷 = 1 2 c m

Q5:

The two triangles in the given figure share the measures of two angles and the length of one side. Does a rigid transformation exist that would map triangle 𝐴 𝐵 𝐶 to triangle 𝐷 𝐸 𝐹 , and, hence, are the two triangles congruent?

  • A yes
  • B no

Q6:

Two triangles have two corresponding angles and one corresponding side that are equal. Are the two triangles congruent?

  • A yes
  • B no

Q7:

Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this.

  • A congruent, SSS
  • B congruent, SAS
  • C not congruent
  • D congruent, ASA

Q8:

Two triangles contain angles of equal measures.

Can we prove that the triangles are similar?

  • Ayes
  • Bno

Can we prove that the two triangles are congruent?

  • Ano
  • Byes

Q9:

In the given figure, a reflection in the line ⃖ ⃗ 𝐴 𝐵 would map triangle 𝐴 𝐵 𝐶 to triangle 𝐴 𝐵 𝐷 . Does it follow that the two triangles congruent?

  • A yes
  • B no

Q10:

Find the length of 𝐸 𝐶 .

Q11:

Are two triangles congruent only when the angles of one triangle are equal to the angles in the other?

  • A No
  • B Yes

Q12:

Triangle has been rotated to obtain triangle as seen in the given figure.

What is the size of ?

  • A
  • B
  • C
  • D

What is the length of ?

  • A5
  • B4
  • C3
  • D2

What is the size of ?

  • A
  • B
  • C
  • D

What type of triangle is ?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q13:

Which is the correct congruence from this figure?

  • A △ 𝐴 𝐵 𝐷 ≅ △ 𝐶 𝐷 𝐴
  • B △ 𝐴 𝐵 𝐷 ≅ △ 𝐴 𝐷 𝐶
  • C △ 𝐴 𝐷 𝐵 ≅ △ 𝐶 𝐷 𝐴
  • D △ 𝐵 𝐷 𝐴 ≅ △ 𝐶 𝐷 𝐴

Q14:

In the given figure, 𝑆 𝑃 = 3 𝑥 − 7 and 𝑆 𝑀 = 2 𝑥 − 2 . Find 𝑆 𝑃 .

Q15:

The triangle in the given figure has been constructed in the following way: is the midpoint of , is the line parallel to , and is the line parallel to .

What do we know about the sizes of angles and ?

  • AAngle is bigger than angle .
  • BAngle is bigger than angle .
  • CThey are equal.

What do we know about the sizes of angles and ?

  • AThey are equal.
  • BAngle is bigger than angle .
  • CAngle is bigger than angle .

What do we know about the lengths of and ?

  • A is longer than .
  • B is longer than .
  • CThey are equal.

Are triangles and congruent? If yes, state by which congruence criteria.

  • Ayes,
  • Byes,
  • Cyes,
  • Dno
  • Eyes,

Therefore, what can be said of the lengths , , , and ?

  • A and
  • B and
  • C and
  • D and
  • E and

Since is a parallelogram, what can be said of the points and ?

  • A is closer to than because is less than .
  • B and are midpoints, because and .
  • CWe cannot conclude anything.
  • D is closer to than because is less than .

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