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

Worksheet: Proving Triangle Congruence Using ASA and AAS Criteria

Q1:

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

  • A yes
  • B no

Q2:

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

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

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:

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

  • A SAS
  • B SSS
  • C ASA

Q5:

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

Q6:

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 𝐡 𝐢 to triangle 𝐷 𝐸 𝐹 , and, hence, are the two triangles congruent?

  • A yes
  • B no

Q7:

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 yes
  • B no

Q8:

Determine the lengths of 𝐴 𝑁 and 𝐡 𝑁 .

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

Q9:

Determine the lengths of 𝐴 𝑁 and 𝐡 𝑁 .

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

Q10:

Find the length of 𝐸 𝐢 .

Q11:

Find the lengths of 𝐢 𝐡 and 𝐴 𝐷 .

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

Q12:

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

  • A no
  • B yes

Q13:

In the following figure, find π‘š ∠ 𝐽 𝐾 𝐿 .

Q14:

Triangle 𝐴 𝐡 𝐢 has been rotated to obtain triangle 𝐴 𝐡 𝐢 β€² β€² β€² as seen in the given figure.

What is the measure of ∠ 𝐴 𝐡 𝐢 ?

What is the length of 𝐴 𝐢 ?

What is the measure of ∠ 𝐴 𝐢 𝐡 ?

What type of triangle is 𝐴 𝐡 𝐢 ?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q15:

Which is the correct congruence from this figure?

  • A β–³ 𝐴 𝐡 𝐷 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 𝐡 𝐷 𝐴 β‰… β–³ 𝐢 𝐷 𝐴

Q16:

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

Q17:

The triangle in the given figure has been constructed in the following way: 𝑀 is the midpoint of 𝐴 𝐡 , 𝑀 𝑃 is the line parallel to 𝐡 𝐢 , and βƒ–       βƒ— 𝑀 𝑄 is the line parallel to 𝐴 𝐢 .

What do we know about the measures of angles 𝐴 𝑀 𝑃 and 𝐴 𝐡 𝐢 ?

  • AAngle 𝐴 𝐡 𝐢 is bigger than angle 𝐴 𝑀 𝑃 .
  • BAngle 𝐴 𝑀 𝑃 is bigger than angle 𝐴 𝐡 𝐢 .
  • CThey are equal.

What do we know about the measures of angles 𝐴 𝑃 𝑀 and 𝑀 𝑄 𝐡 ?

  • AThey are equal.
  • BAngle 𝑀 𝑄 𝐡 is bigger than angle 𝐴 𝑃 𝑀 .
  • CAngle 𝐴 𝑃 𝑀 is bigger than angle 𝑀 𝑄 𝐡 .

What do we know about the lengths of 𝐴 𝑀 and 𝐡 𝑀 ?

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

Are triangles 𝐴 𝑀 𝑃 and 𝐡 𝑀 𝑄 congruent? If yes, state by which congruence criteria.

  • Ayes, 𝐴 𝑆 𝐴
  • Byes, 𝑆 𝐴 𝑆
  • Cyes, 𝑆 𝑆 𝑆
  • Dno
  • Eyes, 𝐴 𝐴 𝐴

Therefore, what can be said of the lengths 𝐴 𝑃 , 𝑀 𝑄 , 𝑀 𝑃 , and 𝐡 𝑄 ?

  • A 𝐴 𝑃 = 𝑀 𝑄 and 𝑀 𝑃 β‰  𝐡 𝑄
  • B 𝐴 𝑃 = 𝐡 𝑄 and 𝑀 𝑃 = 𝑀 𝑄
  • C 𝐴 𝑃 = 𝑀 𝑃 and 𝑀 𝑄 = 𝐡 𝑄
  • D 𝐴 𝑃 = 𝑀 𝑄 and 𝑀 𝑃 = 𝐡 𝑄
  • E 𝐴 𝑃 β‰  𝑀 𝑄 and 𝑀 𝑃 = 𝐡 𝑄

Since 𝑀 𝑃 𝐢 𝑄 is a parallelogram, what can be said of the points 𝑃 and 𝑄 ?

  • A 𝑃 is closer to 𝐴 than 𝐢 because 𝐴 𝑀 is less than 𝑀 𝑃 .
  • B 𝑃 and 𝑄 are midpoints, because 𝐴 𝑃 = 𝑃 𝐢 and 𝐡 𝑄 = 𝑄 𝐢 .
  • CWe cannot conclude anything.
  • D 𝑄 is closer to 𝐡 than 𝐢 because 𝐴 𝑃 is less than 𝑃 𝐢 .