AnswersELPGEQ1 MJ Grade 8 Pre-Algebra - 1205070 HCPS V24Converse to the Pythagorean Theorem

Converse to the Pythagorean Theorem Answers

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Which best explains why this triangle is or is not a right triangle?

Question illustration
A
This triangle is not a right triangle: .
Option A
B
This triangle is not a right triangle: .
Option B
C
This triangle is a right triangle: .
Option C
D
This triangle is a right triangle: .
Option D
2
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Jackie plans to place a rectangular piece of art inside a rectangular frame. She considers a piece of art that is 0.5 meters long, 1.2 meters wide, and has a diagonal length of 1.3 meters.Which is true regarding the art piece?

A
The art is rectangular because .
Option A
B
The art is rectangular because .
Option B
C
The art is not rectangular because .
Option C
D
The art is not rectangular because .
Option D
3

A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation?

A
The foundation cannot be a rectangle: .
Option A
B
The foundation cannot be a rectangle: .
Option B
C
The foundation cannot be a rectangle: .
Option C
D
The foundation may be a rectangle: .
Option D
4

The areas of the squares created by the side lengths of the triangle are shown. Which best explains whether this triangle is a right triangle?[Not drawn to scale]

Question illustration
A
Based on the converse of the Pythagorean theorem, the triangle is a right triangle because .
Option A
B
Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because .
Option B
C
Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because .
Option C
D
Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because .
Option D
5

Which of these four sets of side lengths will form a right triangle?Set 16 cm, 7 cm, cmSet 28 in., in., in.Set 3 mm, 4 mm, mmSet 49 ft, ft, 6 ft

Question illustration
A
Set 1
B
Set 2
C
Set 3
D
Set 4
6

James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1length: 12 in.width: 15 in.diagonal: 20 in.Parallelogram 2length: 16 in.width: 30 in.diagonal: 34 in.Parallelogram 3length: 20 in.width: 21 in.diagonal: 29 in.Parallelogram 4length: 18 in.width: 20 in.diagonal: 26 in.James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle.Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply.

Question illustration
A
The quadrilaterals can be placed such that each occupies one-quarter of the circle.
B
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.
C
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles.
D
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles.
E
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
7

Which math sentence can be used to determine if this triangle is a right triangle?

Question illustration
A
20 + 21 = 29
Option A
B
20 squared + 21 squared = 29 squared
Option B
C
29 + 21 = 20
Option C
D
29 squared + 21 squared = 20 squared
Option D
8

Jude is making a door for a door frame with an opening that measures 9 feet by 3 feet. Which diagonal length should he use to make a door that fits in the door frame?

A
10 feet
B
feet
Option B
C
feet
Option C
D
12 feet
9

Which of these four sets of side lengths will form a right triangle?Set 110 cm, 26 cm, 24 cmSet 24 in., 2 in., 6 in.Set 314 mm, 13 mm, 15 mmSet 410 ft, 30 ft, 20 ft

A
Set 1
B
Set 2
C
Set 3
D
Set 4
10

Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.Step 1:Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches. Step 2: Substitute the values into the Pythagorean theorem: .Step 3:Combine like terms: .Step 4: Evaluate each side: .Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?

Question illustration
A
The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.
B
The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.
C
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
D
The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
11

In an isosceles triangle, the longest side measures c units. The other sides of the triangle measure a units. Which equation can be used to determine if the triangle is a right triangle?

A
a squared = c squared
Option A
B
2 a squared = c squared
Option B
C
a Superscript 4 Baseline = c squared
Option C
D
2 a = c
Option D
12

Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below.Step 1: Step 2: Step 3: Step 4: Which best describes Jeremy’s explanation?

Question illustration
A
Jeremy’s explanation is accurate.
B
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
C
Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.
D
Jeremy’s explanation is inaccurate. He multiplied incorrectly in step 4.
13

Which best explains why this triangle is or is not a right triangle?

Question illustration
A
This triangle is not a right triangle: .
Option A
B
This triangle is not a right triangle: .
Option B
C
This triangle is a right triangle: .
Option C
D
This triangle is a right triangle: .
Option D

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