Geometry: Similar Triangles Quiz

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Questions and Answers

If two triangles are similar, what must be true about their corresponding angles?

They are supplementary.
They are complementary.
They are congruent. (correct)
They are proportional.

Given the proportion $3/2 = y/(y+2)$, what is the value of y?

8
2
4
6 (correct)

What does the term 'ratio' represent in mathematics?

The product of two values.
The comparison of two values, expressed as a fraction. (correct)
The difference between two values.
The sum of two values.

Which of the following correctly describes a 'proportion'?

Two ratios that are equal. (B) Signup and view all the answers

In similar triangles, what is the relationship between their corresponding sides?

They are proportional. (B) Signup and view all the answers

If two triangles are similar, which of the following must be true?

Their corresponding angles are congruent and their corresponding sides are in a constant ratio. (A) Signup and view all the answers

What does 'scale factor' refer to when dealing with similar figures?

The ratio obtained by dividing corresponding side lengths. (A) Signup and view all the answers

Given △ABC and △DEC are similar, if the scale factor of sides from △ABC to △DEC is 2, and AB is 5, what's the length of DE?

10 (D) Signup and view all the answers

If △ABC ~ △DEC, with ∠A = 70° and ∠B = 42°, what is the measure of ∠E?

42° (C) Signup and view all the answers

In the diagram, △GAB ~ △CDO. If GA = 6, CD = 12, and AB = 4, what is the length of DO?

8 (D) Signup and view all the answers

If △RQP ~ △ALN and RQ = 5, QP = 9.5, and AL = 4, what is the length of LN?

7.6 (D) Signup and view all the answers

Given △UTQ ~ △SRQ, RS = 4, UT = 10, and QT = 2x + 10, and RQ = x + 3 what is the value of x?

10 (A) Signup and view all the answers

Using the diagram where △UTQ ~ △SRQ, if RS = 4, UT = 10, find RQ and QT.

RQ = 13, QT = 30 (C) Signup and view all the answers

Using the information provided about the Willis Tower, what proportion can be used to solve the height of the tower?

$12/2 = x/242$ (C) Signup and view all the answers

In the given similar triangles $\triangle MNP$ and $\triangle MRS$, if $MP = 12$, $MR = 18$ and $MS=20$ what is the length of $NP$?

13.33 (A) Signup and view all the answers

In $\triangle MNP$ and $\triangle MRS$, with $MP = 12$ and $MR = 18$, what is the ratio of the sides of the small triangle to the big triangle?

2:3 (D) Signup and view all the answers

What is the proper geometric mean equation to solve for `z` in the figure provided?

$z = \sqrt{24 \cdot 16}$ (D) Signup and view all the answers

Which value is closest to the solution for `y` in the provided figure?

40 (C) Signup and view all the answers

Given the geometric mean relationships, what is the correct calculation to find `x`?

$x= \sqrt{16 \cdot 40}$ (B) Signup and view all the answers

In the Willis Tower problem, if the light pole cast a shadow of 3 feet instead of 2 feet, and the Willis Tower's shadow was still 242 feet, what would the height of the Willis Tower be?

968 feet (B) Signup and view all the answers

If the length of RS is 25, and the length of MP is 12, what is the length of NP?

15 (A) Signup and view all the answers

Flashcards

Ratio

A comparison of two values expressed as a fraction.

Proportion

Two ratios that are equal.