Unit 3, Lesson 13
Using the Pythagorean Theorem and Similarity
Geometry
Practice
Problem 1
In right triangle \(ABC\), altitude \(CD\) is drawn to its hypotenuse. Select all triangles that must be similar to triangle \(ABC\).
\(ABC\)
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In right triangle \(ABC\), altitude \(CD\) is drawn to its hypotenuse. Select all triangles that must be similar to triangle \(ABC\).
\(ABC\)
\(ACD\)
\(BCD\)
\(BDC\)
\(CAD\)
\(CBD\)
In right triangle \(ABC\), altitude \(CD\) with length \(h\) is drawn to its hypotenuse. We also know \(AD=12\) and \(DB=3\). What is the value of \(h\)?
In triangle \(ABC\) (not a right triangle), altitude \(CD\) is drawn to side \(AB\). The length of \(AB\) is \(c\). Which of the following statements must be true?
The measure of angle \(ACB\) is the same measure as angle \(B\).
\(b^2=c^2+a^2\).
Triangle \(ADC\) is similar to triangle \(ACB\).
The area of triangle \(ABC\) equals \(\frac{1}{2}h\boldcdot c\).
Segment \(A’B’\) is parallel to segment \(AB\).
Lines \(BC\) and \(DE\) are both vertical. What is the length of \(AD\)?
4.5
5
7.5
10
Triangle \(DEF\) is formed by connecting the midpoints of the sides of triangle \(ABC\). Select all true statements.
Triangle \(BDE\) is congruent to triangle \(EFC\).
Triangle \(BDE\) is congruent to triangle \(DAF\).
\(BD\) is congruent to \(FE\).
The length of \(BC\) is 8.
The length of \(BC\) is 6.