University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

132

Pages:

2
Author:

Bailey Ayala

Question 1 To determine: Whether the triangle ABC and GHI are similar to each other. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF. Answer △ABC ~ △DEF so, AB/DE = BC/EF = AC/DF △GHI ~ △DEF then, GH/DE = HI/EF = GI/DF If a triangle's sides are similar to one another, then its angles are likewise similar to one another. The triangles △ABC ~ △GHI, the triangle △DEF by SAS similarity, is comparable in both the triangles. As a result, according to SAS similarity, the triangles ABC and GHI are similar to one another. Question 2 To determine:To prove: △RST ~ △XYZ by the SAS similarity theorem. Given: The triangles are similar by theorem SAS. ∠R = ∠X (Given) Answer Calculation: SAS theorem for similarity states that the ratios of two sides of one triangle to the corresponding triangle's two side must be equal. Angle between equal ratios sides of both the triangle must be equal. In triangle RST and XYZ, ∠R = ∠X (Given) Ratios of the sides with end R and X must be equal. Consider the ratios of sides as follows: RS/XY = RT/XZ Hence, the ratios of RS/XY and RT/XZ must be equal to prove △RST ~ △XYZ by SAS similarity theorem. Question 3 To write: the name of the postulate, that justifies the given statement. Given information:In △AVB and △NVK, ∠A = ∠N = 60°. The given figure is as follows: [Image of two triangles labeled AVB and NVK with angle measures and vertices labeled] Answer Angle-Angle similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. In △AVB and △NVK, ∠A=∠N and ∠V is common angle So, △AVB ~ △NVK by Angle-Angle similarity theorem. Hence, the theorem that justifies the given statement is Angle-Angle similarity theorem. Question 4 To prove: The extended proportions that are needed to prove △RST ~ △XYZ by the SSS similarity theorem. Given △RST, △XYZ are two triangles. Answer Calculation: According to the SSS Theorem for Similarity, there must be an equal ratio between the sides of each triangle. In triangle RST and XYZ, Consider the following side ratios: RS/XY, ST/YZ, RT/XZ Hence, the ratios of RS/XY, ST/YZ, and RT/XZ must be equal to prove △RST ~ △XYZ by SSS similarity theorem.