Unit 3, Lesson 16
Finding All the Unknown Values in Triangles
Geometry
Practice
Problem 1
In the right triangles shown, the measure of angle \(ABC\) is the same as the measure of angle \(EBD\). What is the length of side \(BE\)?
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In the right triangles shown, the measure of angle \(ABC\) is the same as the measure of angle \(EBD\). What is the length of side \(BE\)?
In this diagram, lines \(AC\) and \(DE\) are parallel, and line \(DC\) is perpendicular to each of them. What is a reasonable estimate for the length of side \(BE\)?
\(\overleftrightarrow{AC}\parallel \overleftrightarrow{DE}\), \(\overleftrightarrow{DC} \perp \overleftrightarrow{DE }\), \(\overleftrightarrow{DC} \perp \overleftrightarrow{AC}\)
\(\frac{1}{3}\)
1
\(\frac{5}{3}\)
5
Andre says he can find the length of the third side of triangle \(ABC\), and it is 13 units. Mai disagrees and thinks that the side length is unknown. Who do you agree with? Show or explain your reasoning.
In right triangle \(ABC\), altitude \(CD\) with length \(h\) is drawn to its hypotenuse. We also know that \(AD=8\) and \(DB=2\). What is the value of \(h\)?
Right triangle A B C, with horizontal side A B. Vertex C is above side A B and is a right angle. Point D lies on side A B and is directly below vertex C. Altitude C D is drawn. Line segment A D is labeled 2, B D, 8, and C D, h.
Select the sequence of transformations to triangle \(ADE\) that would show that triangles \(ABC\) and \(AED\) are similar. The length of \(AC\) is 6.
\(AC=6\)
Dilate from center \(A\) by a scale factor of \(2\), then reflect over line \(AC\).
Dilate from center \(A\) by a scale factor of \(2\), then rotate 60º around angle \(A\).
Translate by directed line segment \(DC\), then reflect over line \(AC\).
Dilate from center \(A\) by a scale factor of \(4\), then reflect over line \(AC\).