9E: Applying Pythagorean Theorem

9E: Applying Pythagorean Theorem

8th Grade

9 Qs

quiz-placeholder

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9E: Applying Pythagorean Theorem

9E: Applying Pythagorean Theorem

Assessment

Quiz

Mathematics

8th Grade

Medium

CCSS
8.G.B.8, 8.G.B.7, HSG.CO.C.10

+1

Standards-aligned

Created by

Toni Allen

Used 47+ times

FREE Resource

9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The Pythagorean Theorem ONLY works on which triangle?

obtuse

scalene

isosceles

right

Answer explanation

The pythagorean theorem only works for right triangles.

Tags

CCSS.8.G.B.8

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Name the longest side of a right triangle.

leg a

leg b

leg

hypotenuse

Answer explanation

The longest side of a right triangle is the hypotenuse, the side opposite of the right angle.

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The side lengths of a right triangle are 24, 45 and 51. Which side is the hypotenuse?

51

24

45

Can't determine

Answer explanation

The hypotenuse is always the longest side. For a triangle with lengths 24, 45, and 51, 51 is the longest side.

Tags

CCSS.HSG.CO.C.10

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The Pythagorean Theorem is

a2 + b3 = c4

false

true

Answer explanation

The pythagorean theorem for right triangles is: a2+b2=c2a^2+b^2=c^2

Tags

CCSS.8.G.B.8

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the final step in solving this work for c?

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

Divide both sides by 2

Take the square root of both sides

Answer explanation

25=c225=c^2
The next step is to use an inverse operation to "unravel" the exponent above c.

25=c2\sqrt{25}=\sqrt{c^2}
5=c5=c
(Triangles can only have positive side lengths)

Tags

CCSS.8.G.B.8

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Media Image

Find the value of x.

7

8

9

10

Answer explanation

Media Image

a2+b2=c2a^2+b^2=c^2
62+82=x26^2+8^2=x^2
36+64=x236+64=x^2
100=x2100=x^2
100=x2\sqrt{100}=\sqrt{x^2}
10=x10=x

Tags

CCSS.8.G.B.7

7.

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Media Image

Find the missing side (hint: use what you know about estimating irrational numbers to answer)

9

41

6.4

6.2

Answer explanation

Media Image

a2+b2=c2a^2+b^2=c^2
52+42=c25^2+4^2=c^2
25+16=c225+16=c^2
41=c241=c^2
41=c2\sqrt{41}=\sqrt{c^2}

36<41<49\sqrt{36}<\sqrt{41}<\sqrt{49}
6<41<76<\sqrt{41}<7

c6.4c\approx6.4
(is between 6 and 7, slightly closer to 6)

Tags

CCSS.8.G.B.7

8.

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Media Image

Level 2

Solve for the value of y

13

5

23

10

Answer explanation

Media Image

a2+b2=c2a^2+b^2=c^2
y2+122=132y^2+12^2=13^2
y2+144=169y^2+144=169
y2+144144=169144y^2+144-144=169-144
y2=25y^2=25
y2=25\sqrt{y^2}=\sqrt{25}

y=5y=5
(triangles can only have positive side lengths)

Tags

CCSS.8.G.B.7

9.

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Media Image

Find the distance between these two points. Use what you know about pythagorean theorem and estimating irrationals.

6.3

6.5

6.7

16

Answer explanation

Media Image

Distance between y-values, vertical: 3-1 = 2
Distance between x-values, horizontal: 4-(-1) = 6

a2+b2=c2a^2+b^2=c^2

22+62=c22^2+6^2=c^2
4+36=c24+36=c^2
40=c240=c^2
40=c2\sqrt{40}=\sqrt{c^2}

36<40<49\sqrt{36}<\sqrt{40}<\sqrt{49}
6<40<76<\sqrt{40}<7
*between 6 and 7, but closer to 6

c6.3c\approx6.3

Tags

CCSS.HSG.GPE.B.7