Congruence of Triangles

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).

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)

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