FY25 Grade 8 Unit 6: Exploring Geometric Relationships

Jenna wants to hang outdoor stringed lights on her house along the roofline and horizontally across the side of her house, connecting the ends of the roofline to create a triangle.

• A. 48

• B. 64

• C. 80

• D. 98

For a classroom party, there are 12 bottles of fruit punch. Each bottle is filled with 850 cubic centimeters of punch. The fruit punch will be served in cone-shaped paper cups that are 7 centimeters across and 12 centimeters tall. How many completely full cone-shaped cups of punch can be poured?

• A. 16

• B. 66

• C. 232

• D. 265

What is the length of the hypotenuse?

• √11

• √24

• √55

• √73

What is the distance, in units, from point A to point C?

• 3

• √18

• √41

• 9

The coordinate grid shows right triangle ABC and point D. What is the distance, in units, from point A to point D?

• √7

• √14

• 5

• 7

A right triangle is shown in the diagram below. Based on the Pythagorean Theorem, which statement is correct?

• The empty square has a side length of 8 and an area of 64 square units.

• The empty square has a side length of 9.6 and an area of 92 square units.

• The empty square has a side length of 10 and an area of 100 square units.

• The empty square has a side length of 14 and an area of 196 square units.

Which statement is an important part of the proof of the converse of the Pythagorean theorem?

• It must be assumed that the Pythagorean theorem is true.

• It must be assumed that the sum of the lengths of any two sides of a triangle are less than the length of the third side.

• It must be assumed that the Pythagorean theorem is false.

• It must be assumed that the sum of the lengths of any two sides of a triangle are greater than the length of the third side.

This figure is used as part of a visual description of an algebraic statement. Which of the following can be that algebraic statement?

• 1/2(a + b) = c

• a · b = c

Which of the following correctly describes the Pythagorean theorem?

• The sum of the lengths of the legs of a right triangle is equal to the length of the hypotenuse.

• The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

• The product of the lengths of the legs of a right triangle is equal to the length of the hypotenuse.

• The product of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

A new highway was built outside of Tri Town to relieve traffic on Route 1. How many miles are saved by traveling on the new highway to get from point A to point B?

• 1 mile

• 4 miles

• 13 miles

• 30 miles