Proof writing

Question 1

What is the Reflexive Property of Equality?

Answer 1

Any quantity is equal to itself.

Example: a=a

Question 2

What is the Symmetric Property of Equality?

Answer 2

If one quantity equals another, then the second equals the first.

If a=b, then b=a

Question 3

What is the Transitive Property of Equality?

Answer 3

If two quantities are each equal to a third quantity, then they are equal to each other.

If a=b and b=c, then a=c

Question 4

What is the Addition Property of Equality?

Answer 4

You can add the same number to both sides of an equation.

If a=b, then a+c=b+c

Question 5

What is the Subtraction Property of Equality?

Answer 5

You can subtract the same number from both sides of an equation.

If a=b, then a−c=b−c

Question 6

What is the Multiplication Property of Equality?

Answer 6

You can multiply both sides of an equation by the same number.

If a=b, then a⋅c=b⋅c

Question 7

What is the Division Property of Equality?

Answer 7

You can divide both sides of an equation by the same nonzero number.

If a=b and c≠0, then a/c=b/c

Question 8

What is the Substitution Property?

Answer 8

If two things are equal, you can substitute one in place of the other in any expression or equation.

If a=b, then you can replace a with b

Question 9

What is the Reflexive Property of Congruence?

Answer 9

Any geometric figure is congruent to itself.

Example: ∠A≅∠A

Question 10

What is the Symmetric Property of Congruence?

Answer 10

If one figure is congruent to another, then the second is congruent to the first.

If ∠A≅∠B, then ∠B≅∠A

Question 11

What is the Transitive Property of Congruence?

Answer 11

If two figures are each congruent to a third figure, then they are congruent to each other.

If ∠A≅∠B and ∠B≅∠C, then ∠A≅∠C

Question 12

What is the Definition of Congruence?

Answer 12

Two angles or segments are congruent if and only if their measures are equal.

If ∠A≅∠B, then m∠A=m∠B

Question 13

What is the Angle Addition Postulate?

Answer 13

If point B lies inside ∠AOC, then the sum of the smaller angles equals the larger angle.

m∠AOB+m∠BOC=m∠AOC

Question 14

What is the Vertical Angles Theorem?

Answer 14

Vertical (opposite) angles are congruent.

Question 15

What is the Linear Pair Postulate?

Answer 15

If two angles form a linear pair, then they are supplementary (add up to 180°).

If ∠A and ∠B form a straight line, then m∠A+m∠B=180°

Question 16

What is the Right Angle Congruence Theorem?

Answer 16

All right angles are congruent to each other.

If ∠A and ∠B are right angles, then ∠A≅∠B

Question 17

What is the Complementary Angles Theorem?

Answer 17

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

If ∠A+∠B=90° and ∠C+∠B=90°, then ∠A≅∠C

Question 18

What is the Supplementary Angles Theorem?

Answer 18

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

If ∠A+∠B=180° and ∠C+∠B=180°, then ∠A≅∠C

Question 19

What is the Triangle Sum Theorem?

Answer 19

The sum of the interior angles in any triangle is always 180°.

m∠A+m∠B+m∠C=180°

Question 20

What is the Exterior Angle Theorem?

Answer 20

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

m∠D=m∠A+m∠B

Question 21

What is the Base Angles Theorem?

Answer 21

In an isosceles triangle, the angles opposite the equal sides are congruent.

If AB=AC, then ∠B≅∠C

Question 22

What is the Definition of Isosceles Triangle?

Answer 22

A triangle with at least two equal sides and the angles opposite those sides are congruent.

Question 23

What does CPCTC stand for?

Answer 23

Corresponding Parts of Congruent Triangles are Congruent.

Used after you’ve proven two triangles are congruent to show that their parts (angles or sides) are also congruent.

Question 24

What is SSS (Side-Side-Side)?

Answer 24

If all three pairs of corresponding sides of two triangles are congruent, the triangles are congruent.

Question 25

What is SAS (Side-Angle-Side)?

Answer 25

If two pairs of sides and the angle between them in two triangles are congruent, the triangles are congruent.

Question 26

What is ASA (Angle-Side-Angle)?

Answer 26

If two pairs of angles and the side between them in two triangles are congruent, the triangles are congruent.

Question 27

What is AAS (Angle-Angle-Side)?

Answer 27

If two pairs of angles and a non-included side in two triangles are congruent, the triangles are congruent.

Question 28

What is HL (Hypotenuse-Leg)?

Answer 28

In right triangles, if the hypotenuse and one leg are congruent, the triangles are congruent.

Question 29

Perpendicular Bisector Theorem

Answer 29

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Ex: If line CP is the ⊥ bisector of line AB, then angles CA=CB.

Question 30

Converse of Perpendicular Bisector Theorem

Answer 30

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Ex: If angles DA=DB then D is on the ⊥ bisector of line AB.

Question 31

Angle Bisector Theorem

Answer 31

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Ex: If line AD bisects ∠BAC