Polygons
Similar Triangles
Triangles
Side Splitter
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
What type of line is added to a triangle to make the side splitter theorem work?
A line parallel to a side of the triangle.
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
If a triangle has the top left segment of 12 units, the bottom left is 15 units, and the top right is 9 units, what is the length of the final segment?
11.25 units.
200

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

Corresponding, Alternate interior, and alternate exterior.

300
Draw a pair of similar trapezoids.
All angles must be congruent to the corresponding angle and sides are proportional.
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 ZY.

400

A line segment that joins the midpoints of two sides of the triangle is called what?

Midsegment

400

If you divide a parallelogram into four triangles by drawing transversals at its corners, name two kinds of angle congruence you will create.

Vertical angles, Alternate interior angles.

500
Why are all squares similar to each other?
Because by definition the angles are all right and therefore congruent and there is only one side length in a square so it is always the scale factor.
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
Where in real life might the side splitter theorem be useful?
City planning with parallel roads.
500

Fill in the blanks: A midsegment is _____________ to the third side of a triangle and is _____________ the length of the third side.

Parallel, half

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