Deck 2: Parallel Lines

Question 1

Supply missing reasons for this proof.
Given: m || n
Prove: S1. m || n R1.
S2. R2.
S3. R3.
S4. R4.

Answer 1

R1. Given
R2. If 2 parallel line are cut by a transversal, then corresponding angles are congruent.
R3. If two lines intersect, the vertical angles formed are congruent.
R4. Transitive Property of Congruence

Question 2

Use an indirect proof to complete the following problem.
Given: (not shown)
Prove: and cannot both be right angles.

Answer 2

Suppose that and are both be right angles. Then and .
By the Protractor Postulate, . Then . But this last
statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that and cannot both be right angles.

Question 3

Supply missing reasons for the following proof.
Given: with D-B-A
Prove: S1. with D-B-A R1.
S2. R2.
S3. and are supp. R3.
S4. R4.
S5. R5.
S6. R6.

Answer 3

R1. Given
R2. The sum of the interior angles of a triangle is 180.
R3. If the exterior sides of 2 adjacent agles form a line, these angles are supplementary.
R4. Definition of supplementary angles
R5. Substitution Property of Equality
R6. Subtraction Property of Equality

Question 4

Supply missing statements and missing reasons for the following proof.
Given: so that bisects ;
also, Prove: S1. so that bisects R1.
S2. R2.
S3. R3. Given
S4. R4. If 2 angles of one triangle are congruent to
2 angles of a second triangle, then the third angles
of these triangles are also congruent.

Question 5

Supply missing statements in the following proof.
Given: and Prove: S1. R1. Given
S2. R2. If 2 parallel lines are cut by a transversal, corr. angles are congruent.
S3. R3. Given
S4. R4. Same as #2.
S5. R5. Transitive Property of Congruence
S6. R6. If 2 lines are cut by a transversal so that corresponding angles
are congruent, then these lines are parallel.

Question 6

Explain the following statement.
The measure of each interior angle of an equiangular triangle is 60.

Question 7

Supply missing statements and missing reasons for the following proof.
Given: and transversal p; is a right angle
Prove: is a right angle
S1. and transversal p R1.
S2. R2.
S3. R3. Congruent measures have equal measures.
S4. R4.
S5. R5. Substitution Property of Equality
S6. R6. Definition of a right angle

Question 8

In the figure, x || y and transversal z. Explain why and must be supplementary.

Question 9

Supply missing statements and reasons for the foloowing proof.
Given: is supplementary to Prove: S1. R1.
S2. is supp. to R2. If the ext. sides of 2 adj. angles form a line, the angles are supp.
S3. R3. Angles supp. to the same angle are congruent.
S4. R4.

Question 10

In the triangle shown, is a right angle.Explain why and are complementary.

Question 11

Use an indirect proof to complete the following problem.
Given: and are supplementary (no drawing)
Prove: and are not both obtuse angles.

Question 12

Using the drawing provided, explain the following statement.
The sum of the interior angles of a quadrilateral is 360.

Question 13

Use an indirect proof to complete the following problem.
Given: is not congruent to Prove: does not bisect