ID: muniv-pisas Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Standards: HSG-CO.C.11

24 questions

Classroom:
Due:
Student Name:
Date Submitted:
##### True or . . . Sometimes True?: Parallelograms

Given that ﻿$ABCD$﻿ is a parallelogram, decide whether each statement in the first column of the table ﻿$\textbf{must}$﻿ be true, ﻿$\textbf{might}$﻿ be true, or ﻿$\textbf{cannot}$﻿ be true.

1) ﻿$\angle A \cong \angle B$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

2) ﻿$\overline{BD}$﻿ bisects ﻿$\overline{AC}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

3) ﻿$\overline{AD} \cong \overline{BC}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

4) ﻿$\overline{AB}$﻿ intersects ﻿$\overline{CD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

5) ﻿$\overline{AB} \parallel \overline{CD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

6) ﻿$\overline{AB} \cong \overline{AD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

7) ﻿$ABCD$﻿ is a square

a)

Must be true

b)

Could be true

c)

Cannot be true

8) ﻿$\angle B \cong \angle D$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

9) ﻿$\angle A$﻿ is ﻿$90\degree$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

10) ﻿$\overline{AC}$﻿ bisects ﻿$\overline{BD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

11) ﻿$\overline{AD} \parallel \overline{BC}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

12) ﻿$ABCD$﻿ is a pentagon.

a)

Must be true

b)

Could be true

c)

Cannot be true

13) ﻿$\overline{AC} \cong \overline{BD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

14) ﻿$ABCD$﻿ is a rectangle.

a)

Must be true

b)

Could be true

c)

Cannot be true

15) ﻿$\overline{AB} \cong \overline{CD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

16) ﻿$\overline{AB}$﻿ intersects ﻿$\overline{CD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

17) ﻿$\angle A \cong \angle C$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

18) ﻿$\overline{AB} \perp \overline{AD}$﻿

a)

Must be true

b)

Could be true

c)

Cannot be true

19) ﻿$\angle A$﻿ and ﻿$\angle C$﻿ are supplementary to ﻿$\angle B$﻿ and ﻿$\angle D$﻿.

a)

Must be true

b)

Could be true

c)

Cannot be true

Jada is learning about the triangle congruence theorems: Side-Side-Side, Angle-Side-Angle, and Side-Angle-Side. She wonders if there are any theorems like these for parallelograms.

20) If 2 parallelograms have all 4 pairs of corresponding sides congruent, do the parallelograms have to be congruent?

True or false? Write below.

22) In parallelograms ﻿$ABCD$﻿ and ﻿$EFGH$﻿, segment ﻿$AB$﻿ is congruent to segment ﻿$EF$﻿, segment ﻿$BC$﻿ is congruent to segment ﻿$FG$﻿, and angle ﻿$ABC$﻿ is congruent to angle ﻿$EFG$﻿. Are ﻿$ABCD$﻿ and ﻿$EFGH$﻿ congruent?