Finding All the Unknown Values in Triangles

ID: vahot-jujuv
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Finding All the Unknown Values in Triangles

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Problem 1

1) In the right triangles shown, the measure of angle ABCABC is the same as the measure of angle EBDEBD. ​​​What is the length of side BEBE?

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Problem 2

2) In right triangle ABCABC, angle CC is a right angle, AB=13AB = 13, and BC=5BC = 5. What is the length of ACAC?

Problem 3

3) In this diagram, lines ACAC and DEDE are parallel, and line DCDC is perpendicular to each of them. What is a reasonable estimate for the length of side BEBE?

Given: ACDEAC \parallel DE, DCDEDC \perp DE, DCACDC \perp AC

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a) 13 \frac{1}{3} b) 1\text{1}c) 53 \frac{5}{3} d) 5\text{5}
Problem 4

4) Select all of the right triangles. Write each corresponding letter in the answer box and separate letters with commas.

a) Triangle ABCABC with AB=30AB = 30, BC=40BC = 40, and AC=50AC = 50 \quad\quad b) Triangle XYZXYZ with XY=1XY = 1, YZ=1YZ = 1, and XZ=2XZ = 2

c) Triangle EFGEFG with EF=8EF = 8, FG=15FG = 15, and EG=17EG = 17 \quad\quad d) Triangle LMNLMN with LM=7LM = 7, MN=24MN = 24, and LN=25LN = 25

e) Triangle QRSQRS with QR=4QR = 4, RS=5RS = 5, and QS=6QS = 6

Problem 5

Andre says he can find the length of the third side of triangle and it is 13 units. Mai disagrees and thinks that the side length is unknown.

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5) Who do you agree with?

6) Show or explain your reasoning.

Problem 6

7) In right triangle ABCABC, altitude CDCD with length hh is drawn to its hypotenuse. We also know AD=8AD = 8 and DB=2DB = 2. What is the value of hh?

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Problem 7

8) Select the sequence of transformations that would show that triangles ABCABC and AEDAED are similar. The length of ACAC is 6.

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a) Dilate from center A by a scale factor of 2, then reflect over line AC.\text{Dilate from center } A \text{ by a scale factor of 2, then reflect over line } AC \text{.}b) Dilate from center A by a scale factor of 2, then rotate 60º around angle A.\text{Dilate from center } A \text{ by a scale factor of 2, then rotate 60º around angle } A \text{.}c) Translate by directed line segment DC, then reflect over line AC.\text{Translate by directed line segment } DC \text{, then reflect over line } AC \text{.}d) Dilate from center A by a scale factor of 4, then reflect over line AC.\text{Dilate from center } A \text{ by a scale factor of 4, then reflect over line } AC \text{.}