Practice

Prove triangle congruence - Questions

1. Holden tried to prove that \(\triangle F G H \cong \triangle F I H\).

 

  Statement Reason
1 \(\overline{I H} \cong \overline{G H}\) Given
2 \(\overline{F H} \cong \overline{F H}\) Line segments are congruent to themselves. 
3 \(\triangle F G H \cong \triangle F I H\) Side-side congruence

 

What is the first error Holden made in his proof?

Choose 1 answer:

(A) Holden used an invalid reason to justify the congruence of a pair of sides or angles.

(B) Holden only established some of the necessary conditions for a congruence criterion.

(C) Holden established all necessary conditions, but then used an inappropriate congruence criterion.

(D) Holden used a criterion that does not guarantee congruence.

2. Prove that \(\triangle P Q R \cong \triangle S T R\).

 

 

Statement

Reason

1

\(\overline{Q R} \cong \overline{T R}\)

Given

2

\(\overline{P R} \cong \overline{S R}\)

Given

3

Pick statement \((\angle P Q R \cong \angle S T R / \angle R P Q \cong \angle R S T / \angle Q R P \cong \angle T R S)\)

Pick congruence criterion (Angle-angle-side/Angle-side-angle/Side-angle-side/Side-side-side)

4

\(\triangle P Q R \cong \triangle S T R\)

Pick reason (Given/Vertical angles are congruent./Corresponding parts of congruent triangles are congruent).

 

3. Prove that \(\triangle A B C \cong \triangle A D C\).

 

Statement

Reason

1

\(m \angle B A C=m \angle D A C=51^{\circ}\)

Pick statement (Given / Vertical angles are congruent. / Linear pair angles are supplementary).

2

\(A B=A D=4\)

Given

3

Pick statement \(( A B = A B / A C = A C / C D = C D )\)

Segments are the same length as themselves.

4

\(\triangle A B C \cong \triangle A D C\)

Pick congruence criterion (angle-angle-side / Angle-side-angle / Side-angle-side / Side-side-side)

 

4. Jordy tried to prove that \(\triangle A B E \cong \triangle B C D\).

 

 

Statement

Reason

1

\(\angle B C D \cong \angle A B E\)

Given

2

\(\angle C D B \cong \angle B E A\)

Given

3

\(\overleftarrow{B D} \| \overleftrightarrow{A E}\)

Given

4

\(\angle C B D \cong \angle B A E\)

Corresponding angles on parallel lines are congruent.

5

\(\triangle A B E \cong \triangle B C D\)

Angle-angle-angle congruence

 

What is the first error Jordy made in his proof?

Choose 1 answer:

(A) Jordy used an invalid reason to justify the congruence of a pair of sides or angles.

(B) Jordy only established some of the necessary conditions for a congruence criterion.

(C) Jordy established all necessary conditions, but then used an inappropriate congruence criterion.

(D) Jordy used a criterion that does not guarantee congruence.