Finding Missing Lengths in Geometric Figures

This worksheet provides exercises for grade 9 students to practice finding missing lengths in various geometric figures using theorems like the Pythagorean theorem and properties of similar triangles.

Grade 9 Math GeometryFinding Missing Lengths

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Includes

4 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.8.G.B.7CCSS.MATH.CONTENT.HSG.SRT.B.5

Topics

geometrymissing lengthsPythagorean theoremsimilar trianglesgrade 9 math

8 sections · Free to use · Printable

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Finding Missing Lengths

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Read each question carefully and solve for the missing length. Show all your work.

1. Find the length of the hypotenuse of a right triangle with legs measuring 9 cm and 12 cm.

2. A ladder is leaning against a wall. The foot 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 .

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

5. Triangle ABC is similar to Triangle DEF. If AB = 6 cm, BC = 8 cm, and DE = 9 cm, find the length of EF.

6. The sum of the angles in any triangle is always 180 degrees.

True

False

7. In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg.

True

False

8. In a 45-45-90 triangle, if one leg measures 7 units, what is the length of the hypotenuse?