1. Given that ABCD is a parallelogram and AB¯¯¯¯¯¯¯¯∥CD¯¯¯¯¯¯¯¯ , which of the following statements is false?
A. AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯
B. ∠A≅∠C
C. ∠A≅∠B
D. AD¯¯¯¯¯¯¯¯∥BC¯¯¯¯¯¯¯¯
2. Given that ABCD and AFGH are both parallelograms in the image below, which of the following statements is false?
A. ∠GHA≅∠CDA
B. ∠AFG≅∠CDA
C. ∠ABC≅∠FGH
D. ∠BCD≅∠FGH
3. In the parallelogram MNOP , which two sides in the list below are opposite sides?
A. PM¯¯¯¯¯¯¯¯¯ and PO¯¯¯¯¯¯¯¯
B. MO¯¯¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯
C. MN¯¯¯¯¯¯¯¯¯¯ and ON¯¯¯¯¯¯¯¯
D. MN¯¯¯¯¯¯¯¯¯¯ and PO¯¯¯¯¯¯¯¯
4. Given parallelogram WXYZ , determine weather each statement below is true or false
∠X and ∠Y are opposite, congruent angles.
∠X and ∠Z are opposite, congruent angles.
WX¯¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides.
WZ¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides
1. B. ∠A≅∠C (In a parallelogram, opposite angles are congruent, so ∠A and ∠C must be congruent)
2. B. ∠AFG≅∠CDA (In a parallelogram, opposite angles are congruent, so ∠AFG and ∠CDA must be congruent)
3. A. PM¯¯¯¯¯¯¯¯¯ and PO¯¯¯¯¯¯¯¯ (In a parallelogram, opposite sides are congruent, so PM and PO must be congruent)
4. True
- ∠X and ∠Y are opposite, congruent angles (Opposite angles in a parallelogram are congruent)
- ∠X and ∠Z are not opposite angles, so their congruence is not determined
- WX¯¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are not opposite sides, so their congruence is not determined
- WZ¯¯¯¯¯¯¯¯¯ and YX¯¯¯¯¯¯¯¯ are opposite, congruent sides (Opposite sides in a parallelogram are congruent)