Proof for Question 9

pracpf10given
proof10page
 
Statements
  
Reasons
1.
pracpf101
1.
Given
2.
rhombus TRAP is a parallelogramsymbol
pracpf102
2.
A rhombus is a parallelogram with 4 congruent sides.
3.
ΔAPQ congruent ΔPTS
3.
SSS - if 3 sides of 1 Δ are congruentto 3 sides of another Δ, the Δs arecongruent.
4.
∠T congruent ∠APT
4.
CPCTC - corres. parts of congruentΔs arecongruent.
5.
∠T congruent∠PAR;∠APT congruent∠R
5.
Opposite ∠s of a rhombus arecongruent.
6.
∠T supp ∠APT
6.
The consecutive angles of a rhombus are supplementary.
7.
m∠T + m∠APT = 180
7.
Supp. ∠s are 2 ∠s the sum of whose measures = 180.
8.
m∠T = m∠APT
m∠T = m∠PAR
m∠APT = m∠R
8.
congruent∠s have equal measure.
9.
m∠T + m∠T = 180
9.
Substitution
10.
2m∠T = 180
10.
Addition
11.
m∠T = 90;
11.
Division
12.
m∠APT = 90; m∠PAR=90, m∠R = 90
12.
Substitution
13.
∠T, ∠R, ∠APT, ∠PAR rt.∠s
13.
A right ∠ has measure 90.
14.
square TRAP
14.
A square is a parallelogram with 4 congruent sides and 4 right ∠s.

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