Grade 8 | Unit 2 | Lesson 8: Similar Triangles | Practice Problems

In each pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not. Explain how you know. Triangle A: 53, 71, ___; Triangle B: 53, 71, ___

• Similar: They have two pairs of angles with equal measurement.

• Not similar: They do not have two pairs of angles with equal measurement.

Triangle C: 90, 37, ___; Triangle D: 90, 53, ___

• Not similar: Similar triangles have equal angle measurements, and there is no way to fill in the blanks so that this is true for these two triangles.

Triangle E: 63, 45, ____; Triangle F: 14, 71, ____

• Similar: They have equal angle measurements upon calculation completion.

• Not similar: There is no way to make the angles similar.

Triangle G: 121, ___, ___; Triangle H: 70, ___, ___

• Similar: Angles can be made equal.

• Not similar: No triangle can have angles which measure 121 and 70 degrees as these add up to more than 180.

Draw two equilateral triangles that are not congruent. Measure the side lengths and angles of your triangles. Are the two triangles similar? Do you think two equilateral triangles will be similar always, sometimes, or never? Explain your reasoning.

• Cannot be determined from the information given

Describe a sequence of transformations for which Quadrilateral P is the image of Quadrilateral Q. Description:

Two quadrilaterals in an xy plane. Origin 0. Vertical axis from negative 5 to 6 by 1s. Horizontal axis from negative 2 to 12 by 1s. Quadrilateral, labeled P, has points at (3, 3), (6, 6), (4, 1), and (4, 4). Quadrilateral, labeled Q, has points at (7, -4), (12, -6), (10, -3), (10, -4).