Chapter 7 Geometry
The converse of the Pythagorean Theorem says what?
If a triangle follows the formula a2 + b2 = c2, then it must be a right triangle. - The Pythagorean Theorem: Converse and Special Cases
The Right Triangle Altitude Theorem states that _____?
In a right triangle, the altitude drawn to the hypotenuse forms two right triangles that are similar to each other as well as to the original triangle. - Properties of Right Triangles: Theorems & Proofs
The geometric mean gives you the average rate of growth for growth that is what?
Multiplied - Geometric Mean: Definition and Formula
Which of the following is not a right triangle?
NOT 4.5-6-7.5 - The Pythagorean Theorem: Converse and Special Cases
Which of the following statements is correct about the Pythagorean Theorem?
NOT In a right triangle, the sum of the lengths of the legs is equal to the square of the length of the hypotenuse. - Properties of Right Triangles: Theorems & Proofs
Which of the following can the angle bisector theorem help you find?
NOT Missing side lengths - Angle Bisector Theorem: Definition and Example
Which of the following measurements always remains the same in similar polygons?
NOT None - Similar Polygons: Definition and Examples
What numbers cannot be used in geometric mean calculations?
Negative numbers - Geometric Mean: Definition and Formula
Is a half-moon a polygon?
No - What is a Polygon? - Definition, Shapes & Angles
A triangle has side lengths 0.3, 0.4, and 0.5. Do these side lengths form a Pythagorean Triple?
No. Even though 0.3^2 + 0.4^2 = 0.5^2, these lengths are not whole numbers. - The Pythagorean Theorem: Practice and Application
An 14-gon has exterior angles measuring what?
Not enough information. - What is a Polygon? - Definition, Shapes & Angles
When can you use the formula for exterior and interior angles?
Only with regular polygons - What is a Polygon? - Definition, Shapes & Angles
Things are in proportion when what are equal to each other?
Ratios - Solving Problems Involving Proportions: Definition and Examples
If BD = 1, DC = 2, AB = 2, what must AC equal for line segment AD to be an angle bisector?
4 - Angle Bisector Theorem: Definition and Example
If line segment AD is an angle bisector and AB=6, AC = 8, and BD = 3, what must DC equal?
4 - Angle Bisector Theorem: Definition and Example
Find the geometric mean. 4, 4, 4
4 - Geometric Mean: Definition and Formula
Find the geometric mean. 5, 4, 9, 1, 5, 7, 8
4.696 - Geometric Mean: Definition and Formula
A flat screen television has a 50 inch diagonal and a height of 25 inches. How wide is the television?
43.3 inches wide - The Pythagorean Theorem: Practice and Application
If triangle A is similar to triangle B and triangle B is similar to triangle C and if the top angle of triangle C is equal to 45 degrees, what is the measure of the top angle of triangle B?
45 - The Transitive Property of Similar Triangles
Which of the following ratios is not proportional to 2:3?
4:5 - Ratios and Proportions: Definition and Examples
Suppose that the lengths of the legs in a right triangle are 3 and 4. What is the length of the hypotenuse?
5 - Properties of Right Triangles: Theorems & Proofs
Polygon A is 4 times smaller than polygon B. If one side of polygon B measures 20 inches, what does the matching side of polygon A measure?
5 inches - Similar Polygons: Definition and Examples
If two angles of a particular triangle measure 88 and 34, what is the measure of the third angle?
58 - Similar Triangles & the AA Criterion
A regular polygon with 3 sides has interior angles measuring what?
60 - What is a Polygon? - Definition, Shapes & Angles
If an angle in polygon A measures 65 degrees, what does the matching angle in polygon B measure? Polygons A and B are similar polygons.
65 - Similar Polygons: Definition and Examples
A particular pancake recipe calls for 3 cups of flour to 1 cup of milk. Keeping things in proportion, what is the ratio of flour to milk if you double this recipe?
6:2 - Ratios and Proportions: Definition and Examples
Which of the following is proportional to the ratio 3:2?
6:4 - Solving Problems Involving Proportions: Definition and Examples
To make hummingbird food, I need 4 cups of sugar to 1 cup of water. If I wanted to double that amount, how many cups of sugar would I need?
8 - Solving Problems Involving Proportions: Definition and Examples
The sum of the non-right angles of a right triangle is _____?
90 degrees - Properties of Right Triangles: Theorems & Proofs
What line do you need to use the triangle proportionality theorem?
A line parallel to one of the sides of a triangle - Triangle Proportionality Theorem
One triangle has angles that measure 70, 10 and 100 degrees. Which of the following triangles is similar?
A triangle with two angles that measure 100 and 10. - Similar Triangles & the AA Criterion
We have a group of triangles: Triangle A, triangle B, triangle C, triangle D, and triangle E. We are told that triangle B is similar to triangle D and triangle D is similar to triangle A. Which three triangles are similar to each other?
A, B, and D - The Transitive Property of Similar Triangles
According to the AA criterion, how many corresponding angles must be equal for two triangles to be similar?
Two - Similar Triangles & the AA Criterion
Which of the following is the law of cosines?
a2 + b2 - 2*a*b*cos (theta) = c2 - The Pythagorean Theorem: Converse and Special Cases
The Pythagorean Theorem is a special case of what?
law of cosines - The Pythagorean Theorem: Converse and Special Cases
What is the geometric mean of 2 and 4?
2.828 - Geometric Mean: Definition and Formula
Which of the following is not in proportion to the ratio 12:20?
20/30 - Solving Problems Involving Proportions: Definition and Examples
Find the missing information. x/4 = 9/12
3 - Solving Problems Involving Proportions: Definition and Examples
Which of the following is a right triangle?
3-4-5 - The Pythagorean Theorem: Converse and Special Cases
Write a ratio for the number of students who received an A to the number of students who received an F. A Students = 3 B Students = 8 C Students = 2 D Students = 1 F Students = 2
3:2 - Ratios and Proportions: Definition and Examples
A right triangle has one leg that measures 13 centimeters, and the hypotenuse is 17 centimeters. How long is the missing leg?
10.95 centimeters - The Pythagorean Theorem: Practice and Application
Write a ratio for the number of red balls to blue balls. Red balls = 10 Blue balls = 8 Green balls = 6
10:8 - Ratios and Proportions: Definition and Examples
A right triangle has one leg that measures 7 inches, and the second leg measures 10 inches. How long is the hypotenuse?
12.21 inches - The Pythagorean Theorem: Practice and Application
A baseball diamond has 90 feet between each base. How far will the catcher (standing at home plate) throw the ball across the diagonal to the second baseman at 2nd base?
127.28 feet - The Pythagorean Theorem: Practice and Application
Two pentagons are similar. One pentagon has angle measurements of 76, 128, 119, 85, and 132. The other pentagon only has four listed angle measurements of 76, 119, 85, and 132. What is the measure of the missing angle?
128 - Similar Polygons: Definition and Examples
Which of the following ratios is in proportion to the ratio 3:4?
12:16 - Ratios and Proportions: Definition and Examples
A certain regular polygon has an exterior angle measuring 45 degrees. What is the measurement of the polygon's interior angle?
135 - What is a Polygon? - Definition, Shapes & Angles
If line segment AD is an angle bisector and AB = 10, BD = 5, and DC = 7, what does AC measure?
14 - Angle Bisector Theorem: Definition and Example
What do the three angles of a triangle always equal?
180 - Similar Triangles & the AA Criterion
Triangle Proportionality Theorem
AD / DB = AE / EC - Triangle Proportionality Theorem
Complementary angles are _____?
Angles that add up to 90 degrees. - Properties of Right Triangles: Theorems & Proofs
What are congruent angles?
Angles that are equal to each other - Constructing Similar Polygons
With respect to polygons, what are interior angles?
Angles that are inside the polygon - Constructing Similar Polygons
Which of the following is the correct ratio for the angle bisector theorem for this triangle?
BD/DC = AB/AC - Angle Bisector Theorem: Definition and Example
We have a group of triangles: Triangle A, triangle B, triangle C, triangle D, and triangle E. If triangle A is similar to triangle C and triangle C is similar to triangle E, what are the two triangles triangle A is similar to?
C and E - The Transitive Property of Similar Triangles
Which of the following is not a polygon?
Circle - Similar Polygons: Definition and Examples
The corresponding angles of similar polygons are _____?
Congruent - Constructing Similar Polygons
Corresponding angles of similar triangles are always what?
Equal - The Transitive Property of Similar Triangles
Which of the following is the transitive property?
If a = b and b = c then a = c. - The Transitive Property of Similar Triangles
If one side of a larger triangle is three times larger than the corresponding side of a smaller similar triangle, what does this tell you about the other two sides of the triangles?
The other two sides of the larger triangle are also three times larger than the corresponding sides of the smaller triangle. - Similar Triangles & the AA Criterion
The ratio of the lengths of the corresponding sides of similar polygons is _____?
The same - Constructing Similar Polygons
Which of the following is true about similar polygons?
They can be oriented in different ways, as long as the ratio of the lengths of the corresponding sides remains equal and the corresponding angles remain congruent. - Constructing Similar Polygons
