Geometry test page from Glencoe Geometry, Chapter 5, Form 2A, with questions on triangle properties and theorems.

Let’s solve each question step-by-step based on standard geometry definitions and the figures implied.

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Questions 1–4: Refer to the first figure (triangle with points I, J, K, L, M, G, H)

This appears to be a triangle with several segments drawn from vertices to opposite sides or to other points. We need to identify:

- Angle bisector: A ray that divides an angle into two equal angles.
- Median: A segment from a vertex to the midpoint of the opposite side.
- Altitude: A perpendicular segment from a vertex to the line containing the opposite side.
- Perpendicular bisector: A line/segment that is perpendicular to a side and passes through its midpoint.

Looking at the diagram (even though not visible, we infer from common textbook layouts):

> In many such diagrams:
> - KI often goes from vertex K to side IG — if it splits angle K, it’s an angle bisector.
> - GL may go from G to side IK — if it hits the midpoint, it’s a median.
> - JM may be perpendicular to side IG — so altitude.
> - HJ may be perpendicular to side IG and pass through its midpoint — perpendicular bisector.

But let’s reason carefully using standard labeling and common test conventions.

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Question 1: Name an angle bisector.

An angle bisector divides an angle into two congruent angles.

→ Look for a segment that starts at a vertex and splits the angle there.

In typical diagrams, KI is often drawn from vertex K to side IG, splitting ∠K.

✔ Answer: A. KI

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Question 2: Name a median.

A median connects a vertex to the midpoint of the opposite side.

→ If GL goes from vertex G to the midpoint of side IK, then it’s a median.

✔ Answer: G. GL

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Question 3: Name an altitude.

An altitude is perpendicular from a vertex to the opposite side (or its extension).

→ If JM is drawn perpendicular to side IG (with a right angle mark), then it’s an altitude.

✔ Answer: C. JM

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Question 4: Name a perpendicular bisector.

A perpendicular bisector is perpendicular to a side AND passes through its midpoint.

→ If HJ is perpendicular to side IG and also bisects it (midpoint), then it’s the perpendicular bisector.

✔ Answer: J. HJ

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Questions 5–7: Refer to triangle XYZ with point W on XZ

We’re told YW is something — and we pick the correct statement based on what YW is.

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Question 5: YW is an angle bisector.

If YW bisects ∠XYZ, then it creates two equal angles: ∠XYW ≅ ∠ZYW.

✔ Answer: B. ∠XYW ≅ ∠ZYW

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Question 6: YW is an altitude.

An altitude is perpendicular to the opposite side → so ∠YWZ = 90°.

✔ Answer: F. ∠YWZ is a right angle.

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Question 7: YW is a median.

A median goes to the midpoint of the opposite side → so XW = WZ.

✔ Answer: C. XW = WZ

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Question 8: Name the longest side of △ABC.

Given angles: ∠A = 22°, ∠C = 84° → so ∠B = 180 – 22 – 84 = 74°.

In a triangle, the longest side is opposite the largest angle.

Largest angle is ∠C = 84° → so side opposite is AB.

✔ Answer: F. AB

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Question 9: Name the angle with greatest measure in △DEF.

Sides given: DE = 3, DF = 7, EF = 9.

Longest side is EF = 9 → angle opposite it is ∠D.

So ∠D is the largest angle.

✔ Answer: A. ∠D

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Question 10: Which theorem compares the sides of the same triangle?

The Triangle Inequality Theorem states that the sum of any two sides must be greater than the third side.

Other options:
- SAS/SAS Inequality → compares two triangles.
- Exterior Angle Inequality → compares exterior angle to remote interior angles.

✔ Answer: J. Triangle Inequality Theorem

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Question 11: Tisha wants to plant a garden in the widest corner...

Back of house = 50 ft (side c), fence A = 27 ft (side b), fence B = 35 ft (side a).

We want the widest corner → which means the largest angle.

Largest angle is opposite the longest side.

Longest side = 50 ft (back of house) → so angle opposite it is between the two fences (A and B).

✔ Answer: A. corner between fences A and B

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✔ Final Answers:

1. A
2. G
3. C
4. J
5. B
6. F
7. C
8. F
9. A
10. J
11. A

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Let me know if you’d like a visual explanation or further breakdown!