5.12Identify Special Quadrilaterals Example 1 Identify quadrilaterals Quadrilateral ABCD has both pairs of opposite sides congruent. What types of quadrilaterals.

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Presentation transcript:

5.12Identify Special Quadrilaterals Example 1 Identify quadrilaterals Quadrilateral ABCD has both pairs of opposite sides congruent. What types of quadrilaterals meet this condition? Solution There are many possibilities. Opposite sides are congruent. parallelogram rectangle All sides are congruent. rhombus square

5.12Identify Special Quadrilaterals Checkpoint. Complete the following exercises. 1.Quadrilateral JKLM has both pairs of opposite angles congruent. What types of quadrilaterals meet this condition? parallelogram rhombus Opposite angles are congruent. rectangle square All angles are congruent.

5.12Identify Special Quadrilaterals Example 2 Classify a quadrilateral What is the most specific name for quadrilateral ABCD? Solution The diagram shows that both pairs of opposite sides are congruent. By Theorem 5.22, ABCD is a _____________. A D B C parallelogram All sides are congruent, so ABCD is a _________ by definition. rhombus _______ are also rhombuses. However, there is no information given about the angle measures of ABCD. So, you cannot determine whether it is a ________. Squares square

Show that trapezoid FGHJ is __________. F and G are a pair of congruent ____________. So, FGHJ is an _____________________ by Theorem Show that FGHJ is a ___________. G and H are _______________ but F and G are not. 5.12Identify Special Quadrilaterals Example 3 Identify a quadrilateral Is enough information given in the diagram to show that quadrilateral FGHJ is an isosceles trapezoid? Explain. Solution F J G H Step 1 trapezoid supplementary Step 2 isosceles base angles parallel By definition, FGHJ is a _____________. trapezoid isosceles trapezoid Yes, the diagram is sufficient to show that FGHJ is an isosceles trapezoid.

5.12Identify Special Quadrilaterals Checkpoint. Complete the following exercises. 2.What is the most specific name for quadrilateral QRST? Explain your reasoning. Q T R S A kite. By definition it is a quadrilateral with 2 pair of consecutive congruent sides.

5.12Identify Special Quadrilaterals Checkpoint. Complete the following exercises. 3.Is enough information given in the diagram to show that quadrilateral BCDE is a rectangle? Explain. B E C D By Corollary to Theorem 5.16, we know that Both pairs of opposite angles are congruent, so BCDE is a parallelogram by Theorem By definition, BCDE is a rectangle and yes we have enough information.

5.12Identify Special Quadrilaterals Pg. 345, 5.12 #1-24