Congruence of Triangles
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.