Finding Missing Lengths in Geometry

Grade 8 worksheet focusing on finding missing lengths in geometric figures using the Pythagorean theorem and properties of similar triangles.

Grade 8 Math GeometryFinding Missing Lengths

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.8.G.B.7CCSS.MATH.CONTENT.8.G.A.5

Topics

geometrymissing lengthsPythagorean theoremsimilar trianglesgrade 8

7 sections · Free to use · Printable

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Finding Missing Lengths

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Read each question carefully and show all your work. Use the provided diagrams to help you solve for the missing lengths.

1. Find the length of the hypotenuse (c) for a right triangle with legs a = 6 units and b = 8 units.

2. A ladder is leaning against a wall. The base of the ladder is 5 feet from the wall, and the ladder reaches 12 feet up the wall. How long is the ladder?

3. If two triangles are similar, their corresponding sides are and their corresponding angles are .

4. In similar triangles, the ratio of corresponding sides is always .

5. Triangle ABC is similar to Triangle DEF. If AB = 4 cm, BC = 6 cm, and DE = 8 cm, find the length of EF.

6. A tree casts a shadow 15 feet long. A 5-foot tall person standing next to the tree casts a 3-foot shadow. How tall is the tree?

7. Which of the following sets of side lengths could form a right triangle?

3, 4, 6

5, 12, 13

7, 8, 9

4, 5, 6

8. Two triangles are similar if their corresponding angles are:

proportional

congruent

complementary

supplementary

9. The Pythagorean theorem can be used for any triangle.

True

False

10. All equilateral triangles are similar to each other.

True

False