Honors Geometry

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Honors Geometry

• Lesson 6.7
• Congruence and Kites

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What You Should LearnWhy You Should Learn It

• How to prove that two quadrilaterals are
  congruent
• How to identify and use kites to solve problems
• You can use properties of quadrilaterals to solve
  real-life problems, such as proving that a
  real-life kite is actually a geometric kite

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Congruent Quadrilaterals

• Two quadrilaterals are congruent if their
  corresponding angles and corresponding sides are
  congruent

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Theorem 6.22SASAS Congruence Theorem

• If three sides and the included angles of one
  quadrilateral are congruent to the corresponding
  three sides and included angles of another
  quadrilateral, then the quadrilaterals are
  congruent

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Theorem 6.23ASASA Congruence Theorem

• If three angles and the included sides of one
  quadrilateral are congruent to the corresponding
  three angles and included sides of another
  quadrilateral, then the quadrilaterals are
  congruent

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Example 1Proving that Quadrilaterals Are
Congruent

• ABCD and PQRS are parallelograms. Use the given
  measures to prove that the two parallelograms are
  congruent

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Example 1Proving that Quadrilaterals Are
Congruent

• Use SASAS to prove congruence

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Kite

• A kite is a quadrilateral that has two pairs of
  consecutive congruent sides, but opposite sides
  are not congruent.

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Properties of Kites

• Theorem 6.24
• If a quadrilateral is a kite, then its diagonals
  are perpendicular
• Theorem 6.25
• If a quadrilateral is a kite, then exactly one
  pair of opposite angles are congruent

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Example 2Proving that a Quadrilateral is a Kite

• You are building a kite. You have measured the
  cross pieces as shown, and you know that the
  cross pieces meet at right angles. Is your kite a
  true kite?

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Example 2 SolutionProving that a Quadrilateral
is a Kite

• To prove that WXYZ is a kite you must show that

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Example 2 SolutionProving that a Quadrilateral
is a Kite

• To prove that WXYZ is a kite you must show that
• Use indirect reasoning to show that
  

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Example 3

• ABCD and EFGH are kites
• A. What are the lengths of AB and CD?
• B. What are the measures of

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Example 3

• ABCD and GFEH are kites
• A. What are the lengths of AB and CD?
• AB 18 and CD 24
• B. What are the measures of

One pair of opposite angles congruent
360(959590)
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THE END