Warm Up Triangle ADE is an isosceles triangle with the given measures.

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Presentation transcript:

Warm Up Triangle ADE is an isosceles triangle with the given measures. Find the length of side DE. 2)

8-5 Learn to use properties of congruent figures to solve problems. Congruence Learn to use properties of congruent figures to solve problems.

Course 3 8-5 Congruence Vocabulary correspondence

Course 3 8-5 Congruence A correspondence is a way of matching up two sets of objects. If two polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices in the second polygon are written in order of correspondence with the first polygon.

8-5 Congruence Helpful Hint Course 3 8-5 Congruence Marks on the sides of a figure can be used to show congruence. AB @ QR (1 mark) BC @ PR (2 mark) AC @ PQ (3 mark) Helpful Hint __

Additional Example 1A: Writing Congruent Statements Course 3 8-5 Congruence Additional Example 1A: Writing Congruent Statements Write a congruence statement for each pair of polygons. The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence. 55 A corresponds to  . B corresponds to  . C corresponds to  . The congruence statement is triangle ABC @ triangle QRP.

Additional Example 1B: Writing Congruent Statements Course 3 8-5 Congruence Additional Example 1B: Writing Congruent Statements Write a congruence statement for each pair of polygons. The vertices in the first pentagon are written in order around the pentagon starting at any vertex. D corresponds to  . E corresponds to  . F corresponds to  . G corresponds to  . H corresponds to  . The congruence statement is pentagon DEFGH @ pentagon MNOPQ.

8-5 Congruence Check It Out: Example 1A Course 3 8-5 Congruence Check It Out: Example 1A Write a congruence statement for each pair of polygons. The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence. A B | 60° 60° || |||| 120° 120° D ||| C A corresponds to  . Q R ||| 120° 120° B corresponds to  . || |||| C corresponds to  . 60° 60° | D corresponds to  . T S The congruence statement is trapezoid ABCD @ trapezoid STQR.

8-5 Congruence Check It Out: Example 1B Course 3 8-5 Congruence Check It Out: Example 1B Write a congruence statement for each pair of polygons. The vertices in the first pentagon are written in order around the pentagon starting at any vertex. 110° A B A corresponds to  . 110° B corresponds to  . F 140° 140° C 110° C corresponds to  . 110° E D D corresponds to  . N 110° O E corresponds to  . M 110° 140° F corresponds to  . 140° 110° P L The congruence statement is hexagon ABCDEF @ hexagon MNOPQL. 110° Q

Course 3 8-5 Congruence Additional Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY @ quadrilateral JKLM. Find a.

Course 3 8-5 Congruence Additional Example 2B: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY @ quadrilateral JKLM. Find b.

Course 3 8-5 Congruence Additional Example 2C: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY @ quadrilateral JKLM. Find c.

8-5 Congruence Check It Out: Example 2A Course 3 8-5 Congruence Check It Out: Example 2A In the figure, quadrilateral JIHK @ quadrilateral QRST. Find a. 3a I H 6 4b° R S 120° J 30° Q K c + 10° T

8-5 Congruence Check It Out: Example 2B Course 3 8-5 Congruence Check It Out: Example 2B In the figure, quadrilateral JIHK @ quadrilateral QRST. Find b. 3a I H 6 4b° R S 120° J 30° Q K c + 10° T

8-5 Congruence Check It Out: Example 2C Course 3 8-5 Congruence Check It Out: Example 2C In the figure, quadrilateral JIHK @ quadrilateral QRST. Find c. 3a I H 90° 6 4b° R S 90° 120° J 30° Q c + 10° K T

Determine if the two figures are congruent using transformations? Explain the transformation. Translation

Determine if the two figures are congruent using transformations? Explain the transformation. Rotation by 90 followed by translation Rotation

Determine if the two figures are congruent using transformations? Explain the transformation. Reflection across y-axis followed by translation