Deck 3: Triangles

Question 1

Provide missing statements and missing reasons for the proof of the theorem,
"If two sides of a triangle are congruent, then the angles opposite those sides are
also congruent."
Given: with Prove: S1. R1.
S2. Draw the angle bisector for R2. Every angle has exactly one angle-bisector.
S3. R3.
S4. R4.

Answer 1

S1. with R1. Given
R3. The bisector of the vertex angle of an isosceles triangle separates the triangle into
two congruent triangles.
S4. R4. CPCTC

Question 2

Provide mssing statements and missing reasons for the proof of the theorem,
"Corresponding altitudes of congruent triangles are congruent."
Given: ; and Prove: S1. R1.
S2. and R2.
S3. R3. Given
S4. and are rt. R4.
S5. R5. All right angles are congruent.
S6. R6.
S7. R7.

Answer 2

R1. Given
R2. CPCTC
S3. and R4. Perpendicular lines form right angles.
S5. R6. AAS
S7. R7. CPCTC

Question 3

Provide the missing statements and missing reasons for the following proof.
Given: and V is the midpoint of Prove: S1. R1.
S2. R2.
S3. R3. Given
S4. R4.
S5. R5. Identity
S6. R6.
S7. R7.

Answer 3

R1. Given
R2. Perpendicular lines form congruent adjacent angles.
S3. V is the midpoint of R4. Definition of midpoint
S5. R6. SAS
S7. R7. CPCTC

Question 4

In the following problem, explain (prove) why the conclusion is valid..
Given: Quadrilateral with diagonal ; and are right angles
Prove:

Question 5

Supply missing statements and missing reasons for the following proof.
Given: and Prove: S1. R1.
S2. R2. If the measure of one of a is greater than the measure of a
2nd of the , then the side opposite the larger is longer than
the side opposite the smaller .
S3. R3.

Question 6

Explain why the angle-bisector method is justified. Consider that the given angle, ,
is to be bisected by the constructed ray, .

Question 7

Supply missing statements and missing reasons for the following proof.
Given: ; Prove: S1. ; R1.
S2. R2. Identity
S3. R3.

Question 8

Supply missing statements and missing reasons for the following proof.
Given: ; and Prove: is an isosceles triangle
S1. ; R1.
S2. R2.
S3. R3. If 2 angles of a triangle are congruent, the sides
opposite these angles are congruent.
S4. R4.
S5. R5. CPCTC
S6. is an isosceles triangle R6.

Question 9

In the figure provided, . Explain why it is necessary that is also
congruent to

Question 10

Provide missing statements for the following proof.
Given: and are right angles; Prove: S1. R1. Given
S2. R2. All right angles are congruent.
S3. R3. Identity
S4. R4. SAS
S5. R5. CPCTC

Question 11

Provide missing reasons for this proof.
Given: and Prove: bisects S1. and R1.
S2. R2.
S3. R3.
S4, R4.
S5. bisects R5.

Question 12

Provide all statements and all reasons for this proof.
Given: with ; with Prove:

Question 13

Provide missing statements for the following proof.
Given: and Prove: S1. R1. Given
S2. R2. Vertical angles are congruent.
S3. R3. SAS

Question 14

Provide the missing reasons for the following proof.
Given: M is the midpoint of ; also, Prove: S1. M is the midpoint of R1.
S2. R2.
S3. R3.
S4. R4.
S5. R5.

Question 15

Provide missing statements and missing reasons for the following proof.
Given: ; M is the midpoint of and N is the midpoint of Prove: S1. R1.
S2. , , and R2.
S3. R3. Given
S4. R4. The midpoints of two congruent line segments
divide the segments into 4 congruent segments.
S5. R5.
S6. R6.

Question 16

Use the given drawing and information to prove Theorem 3.1.1 (AAS). Provide all
statements and reasons.
Given: , , and Prove: