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

2024
Views:

196

Pages:

4
Author:

Bailey Ayala

Question 1 Explain why the triangle are similar and write a similarity statement. [Image of a triangle labeled ABC with a line segment DE parallel to side BC intersecting sides AB and AC] a.∠A=∠BED and ∠C=∠BDE by the Alternate Interior Angles Theorem. △ABC ~ △EBD by AA Similarity. b.∠A=∠BDE and ∠C=∠BED by the Corresponding Angles Postulate. △ABC ~ △DBE by AA Similarity. c.∠A=∠BDE and ∠C=∠BED by the Corresponding Angles Postulate. △ABC ~ △EBD by AA Similarity. d.∠A=∠BDE and ∠C=∠BED by the Alternate Interior Angles Theorem. △ABC ~ △DBE by AA Similarity. Answer Step 1 Given: Two triangles are given. Step 2 From the given figure: ⇒ ∠A= ∠BDE (Corresponding angles postulate) ⇒ ∠C=∠BED (Corresponding angles postulate) So, ⇒ △ABC ~ △DBE (AA similarity postulate) Option b is correct. Question 2 Determine (if possible) the similarity postulate that proves the following two triangles are similar: SAS similarity postulate There is not enough information to determine whether the triangles are similar or not AA similarity postulate SSS similarity postulate T 58° V 37° U [Image of two triangles labeled TUY and QRS with angle measures labeled] Answer Step 1 In Triangle all angles total is 180 degre. In given triangle both angles are equal then third angle is also equal so all angles are equal then triangle is similar. AA similarly Step 2 AA similar Question 3 Which of the following similarity theorems can be used to compare the two triangles below: a)AA b)SAS c)SSS d)ASA [Image of two triangles labeled APR and AXM with angle and side lengths labeled] Answer So, From the figure, in △APR and △AXM we have AR ~ AM ∠PAR ~ ∠XAM (Vertically opposite angle) AP ~ AX ⇒ △APR ~ △AXM (SAS Theorem) As a result, choice (b) is the right response. Question 4 Tell whether the pair of triangles below is similar and give the reason. [Image of two triangles labeled ABC and ADE with angle measures labeled] Yes, using the Side-Side-Side (SSS) similarity theorem Yes, using the Angle-Angle (AA) similarity postulate No, the triangles are not similar Yes, using the Side-Angle-Side (SAS) similarity theorem Answer Step 1 In the given triangles there are similar angles of 90 degree. It is seen that two rays DC and AE are parallel in the triangle so the alternate interior angle will also be equal in the given triangle. Step 2 From the diagram the consider the alternate interior angles are, m∠DAC ~m∠BAE And the angle m∠D = m∠E = 90° Hence, by AA similarity the two triangles are similar. Hence, the correct option is third one. Yes, using the Angle-Angle (AA) similarity postulate. Question 5 △ABC ~ △KJI. [Image of two triangles labeled ABC and KJI with side lengths labeled and an angle marked.] What is the similarity ratio of △ABC to △KJI? Answer Step 1 Similarity ratio of △ABC → △KJI = AB/KJ = AC/KI Step 2 Simplify: Similarity ratio of △ABC → △KJI = AB/KJ = 2/1 = 2