given: $\overline{ab} \parallel \overline{dc}$ and $\angle b$ and $\angle d$ are right angles
prove: $\angle pqb \cong \angle rsd$

(image of a diagram with points a, b, c, d, p, q, r, s)

| statements | reasons |
| --- | --- |
| $\overline{ab} \parallel \overline{dc}$, and $\angle pbq$ and $\angle rds$ are right angles. | given |
| $\angle b \cong \angle d$ | all right angles are congruent. |
| $\angle bac \cong \angle dca$ | alternate interior angles theorem |
| $\triangle bac \sim \triangle dca$ | aa |
| $\angle bac \cong \angle bpq$ | corresponding angles theorem |
| $\triangle bac \sim \triangle bpq$ | aa |
| $\angle dca \cong \angle drs$ | corresponding angles theorem |
| $\triangle dca \sim \triangle drs$ | aa |
| ? | ? |
| $\angle pqb \cong \angle rsd$ | corresponding angles of similar triangles are congruent. |

which step is missing in the proof?

a. statement: $\triangle bpq \sim \triangle drs$ reason: ssa
b. statement: $\triangle bqp \sim \triangle srd$ reason: hl
c. statement: $\triangle bpq \sim \triangle drs$ reason: transitive property of similarity
d. statement: $\triangle bqp \sim \triangle srd$ reason: reflexive property of similarity

Question

given: $\overline{ab} \parallel \overline{dc}$ and $\angle b$ and $\angle d$ are right angles
prove: $\angle pqb \cong \angle rsd$

(image of a diagram with points a, b, c, d, p, q, r, s)

| statements | reasons |
| --- | --- |
| $\overline{ab} \parallel \overline{dc}$, and $\angle pbq$ and $\angle rds$ are right angles. | given |
| $\angle b \cong \angle d$ | all right angles are congruent. |
| $\angle bac \cong \angle dca$ | alternate interior angles theorem |
| $\triangle bac \sim \triangle dca$ | aa |
| $\angle bac \cong \angle bpq$ | corresponding angles theorem |
| $\triangle bac \sim \triangle bpq$ | aa |
| $\angle dca \cong \angle drs$ | corresponding angles theorem |
| $\triangle dca \sim \triangle drs$ | aa |
| ? | ? |
| $\angle pqb \cong \angle rsd$ | corresponding angles of similar triangles are congruent. |

which step is missing in the proof?

a. statement: $\triangle bpq \sim \triangle drs$ reason: ssa
b. statement: $\triangle bqp \sim \triangle srd$ reason: hl
c. statement: $\triangle bpq \sim \triangle drs$ reason: transitive property of similarity
d. statement: $\triangle bqp \sim \triangle srd$ reason: reflexive property of similarity

Accepted Answer

# Answer:
C. Statement: $	riangle BPQ \sim 	riangle DRS$ Reason: transitive property of similarity

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QUESTION IMAGE

Question

Explanation:

Answer:

statements	reasons
\\(\angle b \cong \angle d\\)	all right angles are congruent.
\\(\angle bac \cong \angle dca\\)	alternate interior angles theorem
\\(\triangle bac \sim \triangle dca\\)	aa
\\(\angle bac \cong \angle bpq\\)	corresponding angles theorem
\\(\triangle bac \sim \triangle bpq\\)	aa
\\(\angle dca \cong \angle drs\\)	corresponding angles theorem
\\(\triangle dca \sim \triangle drs\\)	aa
?	?
\\(\angle pqb \cong \angle rsd\\)	corresponding angles of similar triangles are congruent.