Polygons
Similar Triangles
Triangles
Problem Solving
General Review
100
What is congruent in similar polygons?
Angles
100
What are the three ways you can prove triangles similar?
AA~, SAS~, SSS~
100

Angles of a triangle always sum to how many degrees?

180 degrees

100

Two similar rectangles have widths 4 and 10. If the smaller rectangle’s length is 6, find the larger rectangle’s length.

Scale factor = 10/4 = 2.5

length = 6 × 2.5 = 15

100
Where do you see similar shapes in real life?
Answers vary.
200
How would you describe the relationship between corresponding sides of similar figures?
Proportional.
200

If one triangle has sides of 8 inches and 4 inches and another triangle has sides of 4 inches and 2 inches and the included angles are congruent, what can you conclude about the triangles?

Yes, by SAS~

200
What is a hypotenuse?
The side across from a right angle in a right triangle.
200

A flagpole’s shadow is 8 m long; a nearby 2 m stick casts a 2.5 m shadow. Using similarity, estimate the flagpole’s height.

Stick ratio: height/shadow = 2/2.5 = flagpole/8 → flagpole = 8 × (2/2.5) = 6.4 m

OR  

Scale Factor: 8/2.5 = 3.2

flagpole = 3.2 × 2 = 6.4 m

200

In parallel lines cut by a transversal, what types of angles are congruent?

Corresponding, Alternate interior, and alternate exterior.

300

Name the similarity criterion that requires two pairs of corresponding angles to be equal for triangles to be similar

AA Similarity (AA~)

300

Why do you only need two angles to prove triangles are similar?

The third angle theorem proves that the third angles would also be congruent.

300
If an isosceles triangle has one base angle of 50 degrees, what are the measures of the other two angles?
The other base angle is 50 degrees. The third angle is 80 degrees.
300
What theorem proves the two triangles similar that are created by the side splitter theorem?
AA~
300

If a scale factor is > 1, will a dilated figure reduce or enlarge?

Enlarge

400

Opposite sides of a parallelogram are ______________ and ______________.

Parallel and congruent.

400
The first triangle has sides of 6, 8, and 10. The second triangle has sides of 3, 4, and 6. The third triangle has sides of 9, 12, and 15. Which triangles are similar?
The first and third.
400

If triangle ABC is similar to triangle XYZ, list the congruent parts and the proportional parts.

Angle A is congruent to angle X, Angle B is congruent to angle Y, Angle C is congruent to Angle Z, AB is proportional to XY, BC is proportional to YZ, CA is proportional to ZX.

400

A model car is 1/18 the length of the real car. If the model is 11 inches long, how long is the real car in feet? (Round to nearest tenth.)

Real length = 11 × 18 = 198 in → 198/12 = 16.5 ft.

400

Two parallel lines are cut by a transversal creating corresponding angles. If one corresponding angle is 125°, what is its supplementary interior angle?

Supplementary interior angle = 55° 

(because 180° + 125° = 55°) 

500

Given triangle ABC and triangle DEF with 

∠A = ∠D, ∠B = ∠E, and side AB = 5, side DE = 15, what is the scale factor from ABC to DEF?

3

500
A 3 foot vertical post casts a 24 inch shadow at the same time a pine tree casts a 30 foot shadow. How tall is the pine tree?
45 feet
500

If you know the measure of two sides of a right triangle, how do you find the third side?

Pythagorean Theorem. a^2 + b^2 = c^2

500

A scale drawing of a triangular lot has side lengths 8 cm, 6 cm, and 10 cm. 

The actual lot has a longest side of 250 m. Determine the scale factor and the actual lengths of the other two sides in meters.

Scale factor = 250 m / 10 cm = 25 m per cm if longest side on drawing is 10 cm 

Actual other sides: 8 cm × 25 = 200 m; 

6 cm × 25 = 150 m.

500

Segment XY has length 10. After a dilation with scale factor 0.6, what is the new length?  

10 × 0.6 = 6

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