Question

Triangles unit test 8th grade

Answer 1

Here’s a sample unit test on triangles suitable for an 8th-grade level. It covers concepts such as triangle classification, properties, and the Pythagorean theorem.

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### 8th Grade Triangles Unit Test

**Name: ___________________________ Date: _______________**

**Instructions:** Answer all questions. Show your work where necessary.

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### Part A: Multiple Choice (1 point each)

1. What is the sum of all interior angles in a triangle?
a) 90 degrees
b) 180 degrees
c) 360 degrees
d) 270 degrees

2. Which of the following is NOT a type of triangle based on side lengths?
a) Equilateral
b) Isosceles
c) Scalene
d) Quadrilateral

3. An isosceles triangle has two sides that are:
a) Equal in length
b) Different in length
c) Both longer than the third side
d) Always right angles

4. In a right triangle, the side opposite the right angle is called the:
a) Hypotenuse
b) Adjacent
c) Opposite
d) Altitude

5. If the lengths of two sides of a triangle are 3 cm and 4 cm, what could be the length of the third side?
a) 8 cm
b) 1 cm
c) 4 cm
d) 6 cm

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### Part B: Short Answer (2 points each)

6. Classify the triangle with sides of lengths 5 cm, 5 cm, and 8 cm. Explain your reasoning.

7. If one angle of a triangle measures 50 degrees and another angle measures 60 degrees, what is the measure of the third angle?

8. Using the Pythagorean Theorem, determine if a triangle with sides of 6 cm, 8 cm, and 10 cm is a right triangle.

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### Part C: Problem Solving (3 points each)

9. A triangle has angles measuring 40 degrees and 70 degrees. Calculate the measure of the third angle. Then classify the triangle based on its angles.

10. A triangle has vertices at points A(0,0), B(4,0), and C(0,3). Find the length of each side of the triangle and classify it based on its side lengths.

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### Part D: Application (4 points each)

11. Karen has a triangular garden. The lengths of the sides are 12 feet, 16 feet, and 20 feet. Determine if this is a right triangle. If it is, find the area of the garden.

12. A ladder is leaning against a wall, forming a right triangle with the ground. The foot of the ladder is 4 feet away from the wall and the ladder reaches 10 feet up the wall. How tall is the wall if the ladder reaches a height of 10 feet? Use the Pythagorean theorem to find your answer.

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### Answer Key

- Part A: 1. b, 2. d, 3. a, 4. a, 5. b
- Part B:
6. Isosceles (two sides are equal).
7. 70 degrees (180 - 50 - 60 = 70).
8. Yes, it is a right triangle (6² + 8² = 36 + 64 = 100 = 10²).
- Part C:
9. 70 degrees, Acute triangle (Angle measures are all less than 90 degrees).
10. AB = 4, AC = 3, BC = 5 (3-4-5 triangle, so it is a right triangle).
- Part D:
11. Yes, it's a right triangle (12² + 16² = 400 = 20²). Area = 96 square feet.
12. The height of the wall is 10 feet.

Ensure to adjust questions and answers as necessary to fit the curriculum of your particular school or region!