Congruence for Quadrilaterals

ID: muniv-pisas
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
Standards: HSG-CO.C.11
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24 questions

Congruence for Quadrilaterals

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Student Name:
Date Submitted:
True or . . . Sometimes True?: Parallelograms


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

1) AB\angle A \cong \angle B

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

7) ABCDABCD is a square

a)

Must be true

b)

Could be true

c)

Cannot be true

8) BD\angle B \cong \angle D

a)

Must be true

b)

Could be true

c)

Cannot be true

9) A\angle A is 90°90\degree

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

12) ABCDABCD is a pentagon.

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

14) ABCDABCD is a rectangle.

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

17) AC\angle A \cong \angle C

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

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

a)

Must be true

b)

Could be true

c)

Cannot be true

Floppy Quadrilaterals

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.

21) Explain your reasoning.

22) In parallelograms ABCDABCD and EFGHEFGH, segment ABAB is congruent to segment EFEF, segment BCBC is congruent to segment FGFG, and angle ABCABC is congruent to angle EFGEFG. Are ABCDABCD and EFGHEFGH congruent?

True or false? Write below.

23) Explain your reasoning.

Make Your Own Congruence Theorem

24) Come up with another set of criteria that is enough to be sure that 2 parallelograms are congruent. Use as few measurements as you can.