Geometry Test #4

Question 1

Sum of the Interior Angles of a Triangle and its Corollaries

Answer 1

Recall: The sum of the measures of the interior angles of a triangle is 180.

Corollaries:
1. If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent to each other.
2. The measure of each angle of an equilateral triangle is 60.
3. In a triangle, there can be at most one right angle.
4. The acute angles of a right triangle are complementary.

Question 2

Exterior Angle Theorem

Answer 2

The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 remote interior angles.

Question 3

Exterior Angle Inequality Theorem

Answer 3

The measure of an exterior angle of a triangle is greater than the measure of any of its remote interior angles.

Question 4

Triangle Inequality Theorem

Answer 4

a. The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side.

b. The positive difference of the lengths of any 2 sides of a triangle is less than the length of the third side.

Question 5

Polygon

Answer 5

A polygon is a closed 2D figure formed by straight line segments. Each segment must intersect with exactly 2 other segments at each endpoint. A polygon should have at least 3 sides.

Question 6

Regular Polygon

Answer 6

Equiangular and Equilateral

Question 7

Convex Polygon

Answer 7

All interior angles are less than 180.

Question 8

Concave Polygon

Answer 8

1 or more interior angles is more than 180.

Question 9

Diagonal of a Polygon

Answer 9

A segment joining 2 nonconsecutive vertices.

Question 10

Sum of all interior angles

Answer 10

180(n-2)

Question 11

Measure of one interior angle

Answer 11

180-(360/n)

Question 12

Measure of one exterior angle

Answer 12

360/n

Question 13

Sum of all exterior angles

Answer 13

360

Question 14

If two lines are cut by a transversal,

Answer 14

then corresponding angles are congruent.

Question 15

If two lines are cut by a transversal and corresponding angles are congruent,

Answer 15

then the lines are parallel.

Question 16

Vertical Angles are Congruent

Answer 16

Vertical Angles are Congruent

Question 17

If two lines are perpendicular,

Answer 17

then they form congruent adjacent angles.

Question 18

If two lines form congruent adjacent angles,

Answer 18

then the lines are perpendicular.

Question 19

If the exterior sides of two adjacent acute angles are perpendicular,

Answer 19

then the two angles are congruent

Question 20

If two angles are supplements of congruent angles (or of the same angle),

Answer 20

then the two angles are congruent

Question 21

If two angles are complements of congruent angles (or of the same angle),

Answer 21

then the two angles are congruent

Question 22

3.1
If two parallel planes are cut by a third plane,

Answer 22

then the lines of intersection are parallel.

Question 23

3.2
If two parallel lines are cut by a transversal,

Answer 23

then alternate interior angles are congruent

Question 24

3.3
If two parallel lines are cut by a transversal,

Answer 24

then s-s int. angles are supp..

Question 25

3.4 If a transversal is perpendicular to one of two parallel lines,

Answer 25

then it is perpendicular to the other one also.

Question 26

3.5 If two lines are cut by a transversal and alternate interior angles are congruent,

Answer 26

then the lines are parallel.

Question 27

3.6 If two lines are cut by a transversal and s-s int angles are supp,

Answer 27

then the lines are parallel.

Question 28

In a plane two lines perpendicular to the same line are

Answer 28

parallel

Question 29

3.8 Through a point outside a line,

Answer 29

there is exactly one line parallel to each other.