Question

Two congruent triangles, P Q O and R O Q, overlapping each other. The triangles share a side, line Q O.
Hamza was given this image. He wants to explain why ∠P≅∠R
. He has written the following:

It was given that PQ¯¯¯¯¯¯¯¯≅RO¯¯¯¯¯¯¯¯
and ∠PQO≅∠ROQ
. I also know that QO¯¯¯¯¯¯¯¯≅OQ¯¯¯¯¯¯¯¯
by the _________________________. There is one pair of congruent angles between two pairs of congruent sides, so I know that △OPQ≅△QRO
by the _________________________. This means that ∠P≅∠R
by the _______________.

What phrases should go in the blanks?

(1 point)
Responses

Reflexive Property of Congruence; SAS Congruence Theorem; CPCTC Theorem
Reflexive Property of Congruence; SAS Congruence Theorem; CPCTC Theorem

Reflexive Property of Congruence; CPCTC Theorem; SAS Congruence Theorem
Reflexive Property of Congruence; CPCTC Theorem; SAS Congruence Theorem

CPCTC Theorem; Reflexive Property of Congruence; SAS Congruence Theorem
CPCTC Theorem; Reflexive Property of Congruence; SAS Congruence Theorem

CPCTC Theorem; SAS Congruence Theorem; Reflexive Property of Congruence

Answer 1

The correct phrases to fill in the blanks are:

1. Reflexive Property of Congruence
2. SAS Congruence Theorem
3. CPCTC Theorem

So the full explanation would read:

"It was given that \( PQ \cong RO \) and \( \angle PQO \cong \angle ROQ \). I also know that \( QO \cong OQ \) by the **Reflexive Property of Congruence**. There is one pair of congruent angles between two pairs of congruent sides, so I know that \( \triangle OPQ \cong \triangle QRO \) by the **SAS Congruence Theorem**. This means that \( \angle P \cong \angle R \) by the **CPCTC Theorem**."

Thus, the response would be:

**Reflexive Property of Congruence; SAS Congruence Theorem; CPCTC Theorem**.