Check it out! 1 1.7.1: Proving Triangle Similarity Using SAS and SSS Similarity.

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Check it out! : Proving Triangle Similarity Using SAS and SSS Similarity

Dasha is making earrings to give her friend as a birthday gift. She’s designed a pattern of 3 triangles stacked on top of one another. Dasha is missing some of the measurements for her project. The diagram on the next slide shows Dasha’s design. The given units in the diagram are in centimeters. Use the diagram to answer the questions that follow : Proving Triangle Similarity Using SAS and SSS Similarity

3 1.Are the triangles similar? Explain your answer. 2.Is it possible to determine the missing lengths, x, y, and z? If so, find each value.

1.Are the triangles similar? Explain your answer. Two angles in each triangle are congruent, as noted by the arc marks. According to the Angle-Angle Similarity Statement, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar : Proving Triangle Similarity Using SAS and SSS Similarity

2.Is it possible to determine the missing lengths, x, y, and z? If so, find each value. If two triangles are similar, then the measures of their corresponding sides are proportional, or have a constant ratio. Create a proportion to find each of the unknown values : Proving Triangle Similarity Using SAS and SSS Similarity

Find the value of x : Proving Triangle Similarity Using SAS and SSS Similarity Create a proportion. Substitute. Find the cross products. Simplify. Solve for x. (2)(13.75) = (5)(x) 27.5 = 5x x = 5.5

Find the value of y : Proving Triangle Similarity Using SAS and SSS Similarity Create a proportion. Substitute. Find the cross products. Simplify. Solve for y. (2)(y) = (3.5)(5) 2y = 17.5 y = 8.75

Find the value of z. The missing values for x, y, and z are 5.5 cm, 8.75 cm, and 3.5 cm, respectively : Proving Triangle Similarity Using SAS and SSS Similarity Create a proportion. Substitute. Find the cross products. Simplify. Solve for z. (2)(6.125) = (3.5)(z) = 3.5z z = 3.5