50+ exterior angle property worksheets for 10th Year on Quizizz ... - Free Printable

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

---

Question 1:

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

Diagram: Two intersecting lines 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, since ∠1 and ∠3 are vertical angles:

> ∠1 ≅ ∠3

✔ Correct Answer: B
B) ∠1 ≅ ∠3

> *Explanation:* Vertical angles are always congruent (equal in measure), so we conclude they are congruent.

---

Question 2:

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

- Supplementary angles are two angles whose measures add up to 180°.
- So if ∠1 and ∠2 are supplementary:
> m∠1 + m∠2 = 180°

✔ Correct Answer: D
D) m∠1 + m∠2 = 180°

> *Explanation:* By definition, supplementary angles sum to 180 degrees.

---

Question 3:

Given: $\overline{JN}$ bisects $\overline{ML}$, ∠M ≅ ∠L
What does it mean to bisect a segment or an angle?

- To bisect means to divide into two equal parts.
- For a segment, it means cutting it into two congruent segments.
- For an angle, it means dividing it into two congruent angles.

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

> *Explanation:* "Bisect" comes from Latin *bi-* (two) and *sect* (cut). So it means to cut into two equal parts.

---

Question 4:

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

*(Note: The image is partially cut off, but based on typical geometry proofs involving angles and linear pairs, this likely involves a diagram where two angles form a straight line.)*

Commonly, in such proofs:
- Step 1 might be stating that two angles form a linear pair.
- Step 2 would then use the fact that angles forming a linear pair are supplementary.

So, if:
- Step 1: ∠A and ∠B form a linear pair
- Step 2: Therefore, ∠A and ∠B are supplementary

Then the reason is:

✔ Correct Answer: B
B) Angles that form a linear pair are supplementary.

> *Explanation:* A linear pair consists of adjacent angles that form a straight line (180°), so they must be supplementary.

*(Note: Without seeing the full proof, this is the most logical inference based on common proof structures.)*

---

Question 5:

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

Again, the image is cut off, but let’s assume this is a standard triangle proof or angle proof.

If Step 1 says something like:
> ∠A ≅ ∠A

Then the reason is the Reflexive Property of Congruence — a thing is congruent to itself.

Or if it says:
> m∠A = m∠A

Then it's the Reflexive Property of Equality.

But since it's about congruence, and the answer choices include:

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

And Step 1 is likely stating that an angle is congruent to itself (e.g., in a triangle proof using SAS or ASA), then:

✔ Correct Answer: C
C) Reflexive Property of Congruence

> *Explanation:* This property states that any geometric figure is congruent to itself. Often used in proofs when showing triangles are congruent.

---

✔ Final Answers Summary:

| Question | Answer | Explanation |
|--------|--------|-----------|
| 1 | B | Vertical angles are congruent |
| 2 | D | Supplementary angles add to 180° |
| 3 | D | Bisect means split into 2 equal parts |
| 4 | B | Linear pair → supplementary angles |
| 5 | C | Reflexive Property: a segment/angle is congruent to itself |

---

Let me know if you'd like help with the rest of the 16 questions!