Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Congruence of Triangles: ASA and AAS Criteria

In this lesson, we will learn how to identify congruence in triangles using ASA and AAS criteria and find a missing angle or side length.

Sample Question Videos

03:22

Worksheet • 15 Questions • 1 Video

Q1:

Determine the lengths of 𝐴 𝑁 and 𝐡 𝑁 .

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

Q2:

Determine the lengths of 𝐴 𝑁 and 𝐡 𝑁 .

  • A 𝐴 𝑁 = 4 0 c m , 𝐡 𝑁 = 2 5 c m
  • B 𝐴 𝑁 = 4 0 c m , 𝐡 𝑁 = 1 6 c m
  • C 𝐴 𝑁 = 4 9 c m , 𝐡 𝑁 = 2 5 c m
  • D 𝐴 𝑁 = 4 9 c m , 𝐡 𝑁 = 1 6 c m

Q3:

In the given figure, 𝑆 𝑃 = 3 π‘₯ βˆ’ 7 and 𝑆 𝑀 = 2 π‘₯ βˆ’ 2 . Find 𝑆 𝑃 .

Q4:

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

  • A no
  • B yes

Q5:

Find the length of 𝐸 𝐢 .

Q6:

Which is the correct congruence from this figure?

  • A β–³ 𝐡 𝐷 𝐴 β‰… β–³ 𝐢 𝐷 𝐴
  • B β–³ 𝐴 𝐡 𝐷 β‰… β–³ 𝐴 𝐷 𝐢
  • C β–³ 𝐴 𝐷 𝐡 β‰… β–³ 𝐢 𝐷 𝐴
  • D β–³ 𝐴 𝐡 𝐷 β‰… β–³ 𝐢 𝐷 𝐴

Q7:

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 ?

  • A2
  • B3
  • C5
  • D4

What is the size of ?

  • A
  • B
  • C
  • D

What type of triangle is ?

  • Ascalene
  • Bisosceles
  • Cequilateral

Q8:

Two triangles contain angles of equal measures.

Can we prove that the triangles are similar?

  • Ano
  • Byes

Can we prove that the two triangles are congruent?

  • Ayes
  • Bno

Q9:

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 .
  • BThey are equal.
  • CAngle is bigger than angle .

What do we know about the sizes of angles and ?

  • AAngle is bigger than angle .
  • BThey are equal.
  • CAngle is bigger than angle .

What do we know about the lengths of and ?

  • A is longer than .
  • BThey are equal.
  • C is longer than .

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

  • Ayes,
  • Byes,
  • Cno
  • Dyes,
  • 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 and are midpoints, because and .
  • BWe cannot conclude anything.
  • C is closer to than because is less than .
  • D is closer to than because is less than .

Q10:

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

  • A congruent, 𝐴 𝑆 𝐴
  • B congruent, 𝑆 𝐴 𝑆
  • C not congruent
  • D congruent, 𝑆 𝑆 𝑆

Q11:

In the given figure, a reflection in the line βƒ–     βƒ— 𝐴 𝐡 would map triangle 𝐴 𝐡 𝐢 to triangle 𝐴 𝐡 𝐷 . Does it follow that the two triangles congruent?

  • A no
  • B yes

Q12:

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

  • A SSS
  • B ASA
  • C SAS

Q13:

Find the lengths of 𝐢 𝐡 and 𝐴 𝐷 .

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

Q14:

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

  • A SSS
  • B ASA
  • C SAS

Q15:

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

  • A Yes
  • B No
Preview

Related Lessons