Question 1

Which of the following best describes a ratio?

Accepted Answer

A comparison of two or more quantities.

Question 2

What is the simplified form of the ratio $$24:36$$?

Accepted Answer

$$2:3$$

Question 3

If the extended ratio of the angles in a triangle is $$2:3:4$$, what is the measure of the largest angle?

Accepted Answer

$$80^{\circ}$$

Question 4

Which equation represents a proportion?

Accepted Answer

$$\frac{a}{b} = \frac{c}{d}$$

Question 5

Solve for $$x in $$the proportion $$\frac{4}{x} = \frac{8}{10}.$$

Accepted Answer

$$x = 5$$

Question 6

Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. What is the scale factor if the sides of one triangle are $$6, 8, 10$$ and the corresponding sides of another triangle are $$9, 12, 15$$?

Accepted Answer

$$\frac{3}{2}$$

Question 7

If $$	riangle ABC \sim 	riangle DEF$$ and $$AB = 8$$, $$DE = 12$$, what is the scale factor from $$	riangle ABC to$$ $$	riangle DEF$$?

Accepted Answer

$$\frac{12}{8}$$

Question 8

Given $$	riangle XYZ \sim 	riangle LMN$$, if $$XY = 5$$, $$YZ = 7$$, $$LM = 10$$, and $$MN = 14$$, what is the value of $$XZ if$$ $$LN = 20$$?

Accepted Answer

$$10$$

Question 9

Which similarity criterion requires two pairs of corresponding angles to be congruent?

Accepted Answer

AA (Angle-Angle) Similarity

Question 10

If $$	riangle ABC \sim 	riangle DEF$$ and $$AB = 6$$, $$BC = 9$$, $$DE = 12$$, $$EF = 18$$, what is the value of $$AC if$$ $$DF = 24$$?

Accepted Answer

$$16$$

Question 11

A triangle has sides in the ratio $$3:4:5. If $$the shortest side is $$9$$ units, what is the length of the longest side?

Accepted Answer

$$15$$

Question 12

If two triangles are similar and the scale factor is $$\frac{2}{3}$$, what is the ratio of their corresponding altitudes?

Accepted Answer

$$\frac{2}{3}$$

Question 13

Which property allows you to solve proportions by cross-multiplying?

Accepted Answer

Cross Product Property

Question 14

If $$	riangle ABC$$ and $$	riangle DEF$$ are similar by SSS similarity, which of the following must be true?

Accepted Answer

The ratios of all corresponding sides are equal.

Question 15

In a real-world scenario, a map uses a scale of $$1:50,000. If $$the distance between two cities on the map is $$3 cm$$, what is the actual distance between the cities?

Accepted Answer

$$150,000 cm$$

Question 16

If $$	riangle ABC$$ has sides $$x$$, $$2x$$, and $$3x$$, and $$	riangle DEF$$ has sides $$6$$, $$12$$, and $$18$$, what is the value of $$x if $$the triangles are similar?

Accepted Answer

$$6$$

Question 17

Which theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side?

Accepted Answer

Triangle Proportionality Theorem

Question 18

If an angle bisector in a triangle divides the opposite side into segments of $$3$$ and $$6$$, and the other two sides are $$5$$ and $$10$$, what is the relationship between the sides?

Accepted Answer

$$\frac{3}{6} = \frac{5}{10}$$

Question 19

If three parallel lines intersect two transversals and cut off segments of $$4$$, $$6$$, and $$8 on $$one transversal, what is the length of the corresponding segment on the other transversal if the scale factor is $$2$$?

Accepted Answer

$$8$$, $$12$$, and $$16$$

Question 20

If $$	riangle ABC \sim 	riangle DEF$$ and $$AB = 7$$, $$DE = 14$$, $$BC = 10$$, $$EF = 20$$, what is the value of $$AC if$$ $$DF = 28$$?

Accepted Answer

$$14$$

Ratios, Proportions, and Similarity in Beginning Algebra

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