1.
|
Statements |
Reasons |
| 1. ~~~~~~~~~~~~~~~~~~~~~~~~~ | 1. Given |
| 2. DE is congruent to EC | 2. if isos., then congruent sides |
| 3. AE is congruent to EC, and BE is congruent to ED | 3. if parallelogram, then diag. bis. each other and if bis, then divided into two congruent segments |
| 4. AE is congruent to EB | 4. transitive |
| 5. AC is congruent to DB | 5. Addition Property |
| 6. ABCD is a rectangle | 6. if diag. of parallelogram congruent, then rectangle |
2. AD = 7
3.
|
Statements |
Reasons |
| 1. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | 1. Given |
| 2. AC is congruent to BD, and AD is congruent to BC | 2. if isos. trap., then diagonals congruent and legs congruent |
| 3. DC is congruent to CD | 3. Reflexive |
| 4. Triangle ADC is congruent to triangle BCD | 4. SSS |
| 5. Angle BDC is congruent to angle ACD | 5. CPCTC |
| 6. ED is congruent to EC | 6. if base angles congruent, then legs congruent |
| 7. AE is congruent to EB | 7. Subtraction Property |
| 8. Triangle AEB is isosceles | 8. if legs congruent, then isosceles triangle |
4. P = 48 A = 144 units squared
5. 36
6. a) Always
b) Sometimes
c) Sometimes
d) Sometimes
e) Sometimes
7. m = 23
n = 10