Unit 2, Lesson 12

Proofs about Quadrilaterals

Geometry

Practice

Problem 1

Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that \(EFGH\) is a parallelogram and angle \(HEF\) is right, which reasoning about angles will help her prove that angle \(FGH\) is also a right angle?

<p>Quadrilateral EFGH with angle HEF as a right angle. Line segments EG and HF intersect at point D.</p>

Corresponding angles are congruent when parallel lines are cut by a transversal.
Opposite angles in a parallelogram are congruent.
Vertical angles are congruent.
The base angles of an isosceles triangle are congruent.

Problem 2

\(ABDE\) is an isosceles trapezoid. Select all pairs of congruent triangles.

<p>Isosceles trapezoid A B D E. Angles are marked with tick marks, as follows: D E A, one mark; E A B, two marks; A B D, two tick marks; B D E, one tick mark. Segment A E and B D each have one tick mark.<br>
</p> — \(\overline{AE} \cong \overline{BD} , \angle A \cong \angle B , \angle E \cong \angle D\)

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Proofs about Quadrilaterals

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7