ID: burik-sovop Illustrative Math
Subject: Geometry

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##### Problem 1

Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.

1) Draw a diagram of the situation and mark the given information on the diagram.

2) Restate the conjecture as a specific statement using the diagram.

##### Problem 2

3) In quadrilateral ﻿$ABCD$﻿, ﻿$AD$﻿ is congruent to ﻿$BC$﻿, and ﻿$AD$﻿ is parallel to ﻿$BC$﻿. Show that ﻿$ABCD$﻿ is a parallelogram. ##### Problem 3

4) ﻿$ABDE$﻿ is an isosceles trapezoid. Select all of the statements that could be used to show that the diagonals of an isosceles trapezoid are congruent. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$\triangle ABE \cong \triangle BAD$﻿ ﻿$\quad\quad$﻿ b) ﻿$\triangle ABE \cong \triangle BDE$﻿ ﻿$\quad\quad$﻿ c) ﻿$\triangle AED \cong \triangle BAD$﻿ ﻿$\quad\quad$﻿ d) ﻿$\triangle AED \cong \triangle BDE$﻿ ﻿$\quad\quad$﻿ e) There are none. ##### Problem 4

5) Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other. a) $\text{In parallelogram } EFGH \text{, show triangle } HEF \text{ is congruent to triangle } FGH \text{.}$b) $\text{In parallelogram } EFGH \text{, show triangle } EKH \text{ is congruent to triangle } GKF \text{.}$c) $\text{In parallelogram } EFGH \text{, show } EK \text{ is congruent to } KG \text{ and } FK \text{ is congruent to } KH \text{.}$d) $\text{In parallelogram } EFGH \text{ with } GH \text{ congruent to } FE \text{ and } EH \text{ congruent to } FG \text{, show } EFGH \text{ is a parallelogram.}$
##### Problem 5

6) Is triangle ﻿$EJH$﻿ congruent to triangle ﻿$EIH$﻿?

Given: ﻿$\overline{HJ} \perp \overline{JE}$﻿, ﻿$\overline{HI} \perp \overline{IE}$﻿, ﻿$\overline{HJ} \cong \overline{HI}$﻿ True or false? Write below.

a) Segment ﻿$DC$﻿ is congruent to segment ﻿$AB$﻿. ﻿$\quad\quad$﻿ b) Segment ﻿$DA$﻿ is congruent to segment ﻿$CB$﻿. ﻿$\quad\quad$﻿ c) Line ﻿$DC$﻿ is parallel to line ﻿$AB$﻿. ﻿$\quad\quad$﻿ d) Line ﻿$DA$﻿ is parallel to line ﻿$CB$﻿. ﻿$\quad\quad$﻿ e) Angle ﻿$CBE$﻿ is congruent to angle ﻿$DEA$﻿. ﻿$\quad\quad$﻿ f) Angle ﻿$CEB$﻿ is congruent to angle ﻿$DEA$﻿. a) $\text{All quadrilaterals with 4 equal angles are congruent.}$b) $\text{All quadrilaterals with 4 equal sides are congruent.}$c) $\text{All triangles with 3 equal angles are congruent.}$d) $\text{All triangles with 3 equal sides are congruent.}$