Similar Triangles and Proportions: Geometry Math Quiz – PDF Download
Ten multiple-choice questions check the similarity criteria, the side-splitter theorem and its converse, geometric means in right triangles and indirect measurement. Choose the single best answer, then read the explanation to see the common mistake.
GeometryCommon Core: G-SRT.B.4 · G-SRT.B.5
🎯 Similar Triangles and Proportions – Geometry math quiz
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Question 1
Which condition is NOT enough to prove two triangles similar?
ATwo pairs of congruent angles
BTwo pairs of sides in proportion and a non-included angle congruent
CTwo pairs of sides in proportion and the included angles congruent
DThree pairs of sides in proportion
Question 2
What is the ratio of corresponding sides, larger triangle to smaller?Two triangles with their side lengths.
A\(\frac{2}{3}\)
B\(\frac{3}{2}\)
C\(3\)
D\(5\)
Question 3
In the figure \(DE\) ∥ \(BC\). What is \(x\)?DE is parallel to BC.
A\(10\)
B\(6\)
C\(4\)
D\(9\)
Question 4
Points D and E lie on AB and AC with \(AD=3,\ DB=6,\ AE=4,\ EC=8\). What can you conclude?
ADE is not parallel to BC because AD is not equal to AE
BDE is not parallel to BC because DB is not equal to EC
CDE is parallel to BC because both ratios equal 1/2
DNothing, because angle measures are needed
Question 5
What is the geometric mean of 4 and 25?
A12.5
B14.5
C100
D10
Question 6
In the right triangle, CD is the altitude to the hypotenuse. What is \(CD\)?CD is the altitude to the hypotenuse.
A\(7.5\)
B\(6\)
C\(9\)
D\(36\)
Question 7
One triangle has sides 6 and 8 around a \(40^{\circ}\) angle. Another has sides 9 and 12 around a \(40^{\circ}\) angle. What is true?
AThey are congruent by SAS
BThey are similar by AA with ratio 3/2
CThey are similar by SAS with ratio 3/2
DThey are not similar because 6 is not equal to 9
Question 8
A 6 ft person casts a 4 ft shadow while a tree casts a 30 ft shadow. How tall is the tree?Same time of day.
A45 ft
B20 ft
C34 ft
D36 ft
Question 9
In right triangle ABC with right angle at C and altitude CD, which proportion shows \(AC^{2}=AB\cdot AD\)?
A\(\frac{AB}{AC}=\frac{AC}{AD}\)
B\(\frac{AB}{AC}=\frac{AD}{AC}\)
C\(\frac{AC}{AD}=\frac{CD}{AB}\)
D\(\frac{AD}{AB}=\frac{CD}{AC}\)
Question 10
Triangle ABC is similar to triangle DEF, \(AB=6\), \(DE=15\) and the perimeter of ABC is 21. What is the perimeter of DEF?
A8.4
B30
C52.5
D36
🎉 Quiz complete!
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Remember:
AA, SAS and SSS similarity criteria prove triangles similar (G-SRT.B.4, B.5).
Side-splitter theorem: a line parallel to one side divides the other two sides proportionally, AD/DB = AE/EC; its converse proves lines parallel.
In a right triangle with altitude CD to the hypotenuse, CD squared equals AD times DB.
Each leg is the geometric mean of the hypotenuse and the segment next to that leg.
Similar triangles justify indirect measurement with shadows, mirrors and a proof of the Pythagorean theorem.
