Maya - Geometry Proofs

Question 1

What reason would you give for saying that ∠A ≅ ∠A?

Answer 1

The reflexive property of congruence

Question 2

What reason would you give for saying that ∠A = ∠A?

Answer 2

The reflexive property of equality

Question 3

Given that:
∠A ≅ ∠B
∠B ≅ ∠C
How do you prove that 
∠A ≅ ∠C

Answer 3

The transitive property of congruence

Question 4

Given that m∠A = 45deg

How do you prove that m∠A + 30deg = 45deg + 30deg?

Answer 4

Substitution

Question 5

Given m∠A + 35deg = 180 deg, how would you prove that m∠A = 145deg?

Answer 5

Algebra

Question 6

Given that side AB is perpendicular to side CD, how do you prove that ∠ABC is a right angle?

Answer 6

Definition of perpendicular sides

Question 7

Given that ∠A is a right angle, how do you prove that m∠A = 90deg?

Answer 7

Definition of right angles

Question 8

If ∠A and ∠B form a straight line, how do you prove that ∠A + ∠B = 180deg?

Answer 8

Angles forming a linear pair sum to 180

Question 9

If line AB bisects ∠CBD, how do you prove that ∠CBA ≅ ∠ABD

Answer 9

Definition of angle bisector

Question 10

If line AB bisects line CD through point E, how do you prove that line CE ≅ line ED?

Answer 10

Definition of linear bisector

Question 11

If ∠ABC and ∠CBD are complementary, how do you prove that m∠ABC + m∠CBD = 90 deg?

Answer 11

Definition of complementary angles

Question 12

Given that point U is on line TV, how can you prove that mTV = TU + UV?

Answer 12

Additive property of length

Question 13

What are all the proofs for triangle congruence?

Answer 13

SSS, SAA, ASA, SAS, HL, where sides are congruent and angles are congruent

Question 14

What are all the proofs for triangle similarity?

Answer 14

SSS, SAS, SAA, ASA, HL, and AA where sides are PROPORTIONAL and angles are congruent

Question 15

Given that two lines are parallel, what are all the proofs we know for congruent angles?

Answer 15

Corresponding angles theorem

Alternate exterior angles theorem

Alternate Interior Angles theorem

Vertical Angles theorem

Question 16

If alternating interior angles are NOT congruent, how can we prove that the two lines are not parallel?

Answer 16

The contrapositive of alternate interior angles theorem

Question 17

If alternating interior angles ARE congruent, how can we prove that two lines are parallel?

Answer 17

The converse of alternate interior angle theorem

Question 18

Given “If P, then Q”, what are:

• The converse
• The Inverse
• The Contrapositive

Answer 18

Converse: If Q, then P
Inverse: If not P, then not Q
Contrapositive: If not Q, then not P

Question 19

If triangle ABC is congruent to triangle DEF, how can we prove that ∠A ≅ ∠D?

Answer 19

CPCTC (Congruent parts of congruent triangles are congruent)

Question 20

Given that point C is the midpoint of line AB, how can we prove that m line AC = m line CB

Answer 20

Definition of midpoint