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5.12

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

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5.12

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

  2. 5.12 Identify Special Quadrilaterals Opposite angles are congruent. All angles are congruent. Checkpoint. Complete the following exercises. • Quadrilateral JKLM has both pairs of opposite angles congruent. What types of quadrilaterals meet this condition? square rectangle parallelogram rhombus

  3. 5.12 Identify Special Quadrilaterals B A D C Classify a quadrilateral Example 2 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 _____________. parallelogram rhombus All sides are congruent, so ABCD is a _________ by definition. Squares _______ are also rhombuses. However, there is no information given about the angle measures of ABCD. So, you cannot determine whether it is a ________. square

  4. 5.12 Identify Special Quadrilaterals G F H J Show that FGHJ is a ___________. G and H are _______________ but F and G are not. Show that trapezoid FGHJ is __________. F and G are a pair of congruent ____________. So, FGHJ is an _____________________ by Theorem 5.30. Identify a quadrilateral Example 3 Is enough information given in the diagram to show that quadrilateral FGHJ is an isosceles trapezoid? Explain. Solution trapezoid Step 1 supplementary parallel trapezoid By definition, FGHJ is a _____________. isosceles Step 2 base angles isosceles trapezoid Yes, the diagram is sufficient to show that FGHJ is an isosceles trapezoid.

  5. 5.12 Identify Special Quadrilaterals 8 Q R 7 8 T 7 S Checkpoint. Complete the following exercises. • What is the most specific name for quadrilateral QRST? Explain your reasoning. A kite. By definition it is a quadrilateral with 2 pair of consecutive congruent sides.

  6. 5.12 Identify Special Quadrilaterals C B By Corollary to Theorem 5.16, we know that D E Checkpoint. Complete the following exercises. • Is enough information given in the diagram to show that quadrilateral BCDE is a rectangle? Explain. Both pairs of opposite angles are congruent, so BCDE is a parallelogram by Theorem 5.23. By definition, BCDE is a rectangle and yes we have enough information.

  7. 5.12 Identify Special Quadrilaterals Pg. 345, 5.12 #1-24

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