Illustrative Mathematics - Geometry - Mathematics - Unit 2 - Lesson 13 - Formative Library | Library

Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.
Draw a diagram of the situation.
Mark the given information.
Restate the conjecture as a specific statement using the diagram.

G.CO.9

G.CO.11

G.CO.8

In quadrilateral ABCD, AD is congruent to BC, and AD is parallel to BC. 
Show that ABCD is a parallelogram.

G.CO.9

G.CO.11

G.CO.8

ABDE is an isosceles trapezoid. Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles trapezoid are congruent.

G.CO.9

G.CO.11

G.CO.8

Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.

In parallelogram EFGH, show triangle HEF is congruent to triangle FGH.

In parallelogram EFGH, show triangle EKH is congruent to triangle GKF.

In parallelogram EFGH, show EK is congruent to KG and FK is congruent to KH.

In quadrilateral EFGH with GH congruent to FE and EH congruent to FG, show EFGH is a parallelogram.

G.CO.9

G.CO.11

G.CO.8

Is triangle EJH congruent to triangle EIH?

Explain your reasoning.

G.CO.9

G.CO.11

G.CO.8

Select all true statements based on the diagram.

Segment DC is congruent to segment AB.

Segment DA is congruent to segment CB.

Line DC is parallel to line AB.

Line DA is parallel to line CB.

Angle CBE is congruent to angle DEA.

Angle CEB is congruent to angle DEA.

G.CO.9

G.CO.11

G.CO.8

Which conjecture is possible to prove?

All quadrilaterals with 4 equal angles are congruent.

All quadrilaterals with 4 equal sides are congruent.

All triangles with 3 equal angles are congruent.

All triangles with 3 equal sides are congruent.

G.CO.9

G.CO.11

G.CO.8

This lesson is from Illustrative Mathematics. Geometry, Unit 2, Lesson 13. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/2/13/index.html ; accessed 29/July/2021.

IM Algebra 1, Geometry, Algebra 2 is © 2019 Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

These materials include public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.