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

Worksheet: Proving Triangles' Congruence Using ASA and AAS Criterions

This worksheet assesses how to identify congruence in triangles and describe the criteria of congruence. It has many questions to identify ASA and AAS criterions and find a missing angle or side length.

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,
  • B congruent,
  • C not congruent
  • D congruent,

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 to triangle , and, hence, are the two triangles congruent?

  • A yes
  • B no

Q7:

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

  • A yes
  • B no

Q8:

Determine the lengths of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q9:

Find the length of .

Q10:

Find the lengths of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q11:

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

  • A no
  • B yes

Q12:

In the following figure, find .

Q13:

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

What is the measure of ?

What is the length of ?

What is the measure of ?

What type of triangle is ?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q14:

Use the figure to determine .

  • A
  • B
  • C
  • D

Q15:

Find the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q16:

Find the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q17:

Which is the correct congruence from this figure?

  • A
  • B
  • C
  • D

Q18:

In the given figure, and . Find .