Geometry proofs worksheet from Quizizz with multiple-choice questions on angle relationships and proofs.

Let's go through each of the first five questions from your Quizizz Geometry Proofs worksheet and solve them step by step with explanations.

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Question 1:

> Given: ∠1 and ∠3 are vertical angles. What should you conclude by the vertical angles theorem?

Diagram: Two lines intersecting, forming four angles labeled ∠1, ∠2, ∠3, ∠4.

- Vertical angles are the angles opposite each other when two lines cross.
- The Vertical Angles Theorem states that vertical angles are congruent.

So, if ∠1 and ∠3 are vertical angles, then:
> ∠1 ≅ ∠3

✔ Correct Answer: B) ∠1 ≅ ∠3

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Question 2:

> Given: ∠1 and ∠2 are supplementary. What can you conclude?

Definition: Supplementary angles are two angles whose measures add up to 180°.

So:
> m∠1 + m∠2 = 180°

✔ Correct Answer: D) m∠1 + m∠2 = 180°

Note: Just because they are supplementary doesn't mean they are equal or right angles — only that their sum is 180°.

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Question 3:

> What does it mean to bisect a segment or an angle?

Bisect means to divide into two equal parts.

- A segment bisector cuts a segment into two equal segments.
- An angle bisector divides an angle into two congruent angles.

✔ Correct Answer: D) Split it into 2 equal parts.

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Question 4:

> In the given proof, what are the reasons for step 1 and 2?

⚠️ *Note: The image for this question is partially cut off (the proof table is not fully visible), so we must infer based on typical geometry proofs.*

But since we don’t see the actual steps, let’s consider common reasoning in proofs involving angles:

If step 1 involves stating that two angles are congruent because they have equal measures → that would be:
> Angles of equal measure are congruent → Option A

If step 2 involves angles forming a straight line (linear pair), then:
> Angles that form a linear pair are supplementary → Option B

But without seeing the exact proof, we can't be 100% sure. However, based on standard proofs (especially those involving triangle congruence or parallel lines), these are common early steps.

Assuming:
- Step 1: "Given: m∠A = m∠B" → So, ∠A ≅ ∠B → Reason: Angles of equal measure are congruent (Option A)
- Step 2: Two angles form a straight line → So they are supplementary → Reason: Angles that form a linear pair are supplementary (Option B)

✔ Likely Correct Answer: A and B

But wait — the question says “what are the reasons for step 1 and 2?” and gives options as single choices. That suggests maybe it's asking for one reason that applies to both? Or perhaps it's multiple choice with combinations?

Looking at the layout, it seems like only one answer can be selected, but the options are listed separately.

Wait — actually, looking again:

> A) Angles of equal measure are congruent
> B) Angles that form a linear pair are supplementary
> C) Reflexive Property of Congruence
> D) Substitution

And the question asks: “What are the reasons for step 1 and 2?”

Since only one option can be chosen, and it's likely that both steps involve different reasoning, perhaps the image shows a specific proof where Step 1 uses reflexive property (e.g., a segment is congruent to itself), and Step 2 uses substitution.

But without the diagram, we’re guessing.

However, if the proof is about proving triangles congruent using SAS or ASA, and step 1 says something like “JK ≅ JK”, then the reason is:
> Reflexive Property of Congruence → Option C

Then step 2 might use substitution.

But again, no visual.

Let’s suppose the proof is about vertical angles, and step 1 is “m∠1 = m∠3” (given), and step 2 is “∠1 ≅ ∠3”.

Then reason for step 2 would be: Angles of equal measure are congruent → Option A

Alternatively, if step 1 is “∠1 and ∠2 form a linear pair”, then reason is: Angles that form a linear pair are supplementary → Option B

But since we can’t see the proof, and this is a common type, here’s a safe assumption:

👉 If step 1 is saying two angles are congruent because they have the same measure → A
👉 If step 2 is showing substitution (e.g., replacing an angle with another congruent one) → D

But again, we need more info.

But wait — option C is Reflexive Property of Congruence — that’s often used when a side or angle is shared between two triangles (like side JK in both triangles).

If step 1 is: “JK ≅ JK”, then reason is C.

If step 2 is: “Substitute known values” → D

But since the question asks for reasons for step 1 and 2, and only one choice is allowed, perhaps the correct answer is C, if step 1 is reflexive.

Alternatively, maybe the image shows a proof where step 1 is “∠1 ≅ ∠3” due to vertical angles, so reason is congruent angles → A

But without seeing it, it's hard.

But let’s assume the most common scenario: In many proofs, step 1 is the reflexive property (e.g., a side is congruent to itself), and step 2 is substitution.

But again, not enough info.

Wait — look at question 5: It mentions “In the given proof, what is the reason for step 1?” — so there’s a proof shown.

But since the image is cut off, we can’t see it.

So for now, we cannot definitively answer Q4 and Q5 without seeing the proof.

But let’s try to deduce.

Perhaps the proof is:

1. ∠M ≅ ∠L (Given)
2. ∠M and ∠L are right angles → so m∠M = m∠L = 90°
3. Then conclusion...

But still unclear.

Alternatively, if the proof is about triangle congruence, and step 1 is “JK ≅ JK”, then:

✔ Answer: C) Reflexive Property of Congruence

That’s very common.

So unless the proof shows otherwise, likely answer is C.

But again — without seeing the proof, we're limited.

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Question 5:

> In the given proof, what is the reason for step 1?

Same issue — proof not visible.

But if step 1 is something like:
> “Given: ∠A ≅ ∠B”

Then reason is Given — but that’s not an option.

Options aren’t listed here either — probably missing.

So we can’t answer Q4 and Q5 accurately without the full image.

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✔ Final Answers (based on available info):

| Question | Answer | Explanation |
|--------|--------|-----------|
| 1 | B | Vertical angles are congruent. |
| 2 | D | Supplementary angles add to 180°. |
| 3 | D | To bisect means to split into two equal parts. |
| 4 | C *(assumed)* | Likely reflexive property if step 1 is a shared side. |
| 5 | Not determinable | Proof not visible. |

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🔍 Recommendation:

Please upload the full image or describe the proof steps for questions 4 and 5 so I can give accurate answers.

For now, here are the definitive answers for questions 1–3:

> 1. B
> 2. D
> 3. D

For 4 and 5, please provide more details!