Find the unknown side lengths labeled with a variable in each pair of similar right triangles.
What is side length "a"?
Find the unknown side lengths labeled with a variable in each pair of similar right triangles.
What is side length "a"?
1.2 Angle Relationships and Similar Triangles
Concept Check Name the corresponding angles and the corresponding sides of each pair of similar triangles.
There are several exercises involving similar triangles, unknown angle measures, and unknown side lengths. Refer to each diagram as you answer the questions.
Find the unknown side lengths labeled with a variable in each pair of similar right triangles.
What is side length "a"?
Find the unknown side lengths labeled with a variable in each pair of similar right triangles.
What is side length "b"?
What is the measure of angle A?
Answer:
An isosceles triangle has two equal side lengths of 12 and a base of 15. A similar triangle has two equal side lengths of 6. What is the similar triangle's base?
Two similar triangles are given. What is the value of x?
Height of a Tree A tree casts a shadow 45 m long. At the same time, the shadow cast by a vertical 2-m stick is 3 m long. Using similar triangles, find the height of the tree. ___ meters
Lengths of Sides of a Triangle On a photograph of a triangular piece of land, the lengths of the three sides are 4 cm, 5 cm, and 7 cm, respectively. The shortest side of the actual piece of land is 400 m long. Assuming the photograph and the actual land form similar triangles, find the lengths of the other two sides of the actual land.
Height of a Building A house is 15 ft tall. Its shadow is 40 ft long at the same time the shadow of a nearby building is 300 ft long. Assuming the sun’s rays form similar triangles with the house and the building, find the height of the building. ____ feet
In each diagram, there are two similar triangles. Find the unknown measurement. (Hint: In the sketch for this exercise, the side of length 100 in the small triangle corresponds to the side of length 
Use the following diagram to find the unknown measurement for this exercise.
In each diagram, there are two similar triangles. Find the unknown measurement using the diagram below. Round your answer to the nearest tenths place.
CHALLENGE!
Lengths of Sides of a Quadrilateral Two quadrilaterals (four-sided figures) are similar. The lengths of the three shortest sides of the first quadrilateral are 18 cm, 24 cm, and 32 cm. The lengths of the two longest sides of the second quadrilateral are 48 cm and 60 cm. Work the problem and find the unknown lengths of the sides of these two figures. Explain how you used similarity ratios.