Question

Given: Lines p and q are parallel and r is a transversal. Prove: ∠2 ≅ ∠7 Which statements could complete the proof? A: B:

Answer 1

Answer:

A: Angle 2 is congruent to angle 3

B: Angle 3 is congruent to angle 7

Step-by-step explanation:

Answer 2

$\angle 2$ and $\angle 7$ are congruent angles based on corresponding and vertical angle theorems.

The statements that complete the proof are:

$2.\ \angle 2 \cong \angle 3$

$3.\ \angle 3 \cong \angle 7$

See attachment for the table of proof to complete.

We have:

$1. p || q;\ r\ is\ a\ transv \to$ Given

From the attached diagram

$\angle 2$ and $\angle 3$ are vertical angles.

So:

$2.\ \angle 2 \cong \angle 3 \to$ Vertical angles theorem

Also, from the diagram;

$\angle 3$ and $\angle 7$ are corresponding angles.

So:

$3.\ \angle 3 \cong \angle 7 \to$ Corresponding angle theorem

Transitive property of equality states that:

If $a = b$ and $b =c$, then:

$a = c$

So, we have:

$4.\ \angle 2 \cong \angle 7 \to$ Transitive property

Hence, the statements that complete the proof are:

$2.\ \angle 2 \cong \angle 3$

$3.\ \angle 3 \cong \angle 7$

Read more about proofs at:

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