Transformations and Similarity Unit Test
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Question
Use the image to answer the question.
An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.
What is the length of x in decimal form to the nearest hundredth?
(1 point)
inches
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To find the length of x, we can set up a proportion between the small triangle and the big triangle:
11.4/18 = x/23.4
Cross multiplying, we get:
18x = 11.4 * 23.4
18x = 266.76
x = 266.76/18
x = 14.82
So, the length of x in decimal form to the nearest hundredth is 14.82 inches.
△CDE∼△PQR. m∠C=13°, m∠D=65°. What are the measures of angles P, Q, and R?(2 points)
m∠P =
°, m∠Q =
° and m∠R=
°
Since triangles CDE and PQR are similar, corresponding angles are equal.
m∠C = m∠P and m∠D = m∠Q
Given that m∠C = 13° and m∠D = 65°:
m∠P = 13°
m∠Q = 65°
Now, since the sum of angles in a triangle is 180° and these two angles are known, we can find m∠R:
m∠R = 180 - m∠P - m∠Q
m∠R = 180 - 13 - 65
m∠R = 102°
Therefore, the measures of angles P, Q, and R are:
m∠P = 13°
m∠Q = 65°
m∠R = 102°
△XYZ∼△RST . m∠X=50° , m∠S=79° . What is the measure of angle T ?(1 point)
m∠T =
°
Since triangles XYZ and RST are similar, corresponding angles are equal.
m∠X = m∠R and m∠S = m∠T
Given that m∠X = 50° and m∠S = 79°:
m∠R = 50°
m∠T = 79°
Therefore, the measure of angle T is:
m∠T = 79°