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Worksheet: Proving Triangles' Congruence Using ASA and AAS Criterions

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 .