Answer:
Step-by-step explanation:
11. If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram.
∠J ≅ ∠ L (congruent ∠s have equal measures.)
9y+1 = 10y-13
when y = 14
9(14)+1 = 10(14)-13
126+1 = 140-13
127 ≅ 127 (congruent ∠s have equal measures.)
or
THEOREM: If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram.
∠K + ∠ L = 180° ( angles are supplementary )
(10y-13) + (7x+4) = 180
10y-13+7x+4 = 180°
y=14 x =7
10(14) -13 + 7(7) + 4 = 180
140 - 13 + 49 + 4 = 180
rearrange the plus sign
140+49+4-13=180
193-13=180
180≅180
9
12.
If a quadrilateral has diagonals that bisect each other, then it is a parallelogram.
IADI = IBCI
IDCI = IABI
therefore IACI = IBDI = 25
corres. parts of congruent triangles are congruent.
13. If a parallelogram has perpendicular diagonals, it is a rhombus.
∠PQR=∠PSR= 2x+3
All right angles are congruent.
