CHAPTER 8 Geometry Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1Basic Geometric Figures 8.2Perimeter 8.3Area 8.4Circles 8.5Volume.

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Presentation transcript:

CHAPTER 8 Geometry Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1Basic Geometric Figures 8.2Perimeter 8.3Area 8.4Circles 8.5Volume and Surface Area 8.6Relationships Between Angle Measures 8.7Congruent Triangles and Properties of Parallelograms 8.8Similar Triangles

OBJECTIVES 8.7 Congruent Triangles and Properties of Parallelograms Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aIdentify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. bUse properties of parallelograms to find lengths of sides and measures of angles of parallelograms.

8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8.7 Congruent Triangles and Properties of Parallelograms CONGRUENT TRIANGLES Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Two triangles are congruent if and only if their vertices can be matched so that the corresponding angles and sides are congruent.

8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The corresponding sides and angles of two congruent triangles are called corresponding parts of congruent triangles. Corresponding parts of congruent triangles are always congruent.

8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 3 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Suppose that What are the congruent corresponding parts?

8.7 Congruent Triangles and Properties of Parallelograms THE SIDE–ANGLE–SIDE (SAS) PROPERTY Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 5 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Which pairs of triangles on the next slide are congruent by the SAS property? Pairs (b) and (c) are congruent by the SAS property.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 5 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8.7 Congruent Triangles and Properties of Parallelograms THE SIDE–SIDE–SIDE (SSS) PROPERTY Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 6 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Pairs (b) and (d) are congruent by the SSS property. Which pairs of triangles are congruent by the SSS property?

8.7 Congruent Triangles and Properties of Parallelograms THE ANGLE–SIDE–ANGLE (ASA) PROPERTY Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 7 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Which pairs of triangles are congruent by the ASA property? Pairs (b) and (c) are congruent by the ASA property.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 13 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms a Identify the corresponding parts of congruent triangles and show why triangles are congruent using SAS, SSS, and ASA. 14 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8.7 Congruent Triangles and Properties of Parallelograms PROPERTIES OF PARALLELOGRAMS Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. A diagonal of a parallelogram determines two congruent triangles. 2. The opposite angles of a parallelogram are congruent. 3. The opposite sides of a parallelogram are congruent. 4. Consecutive angles of a parallelogram are supplementary. 5. The diagonals of a parallelogram bisect each other.

EXAMPLE 8.7 Congruent Triangles and Properties of Parallelograms b Use properties of parallelograms to find lengths of sides and measures of angles of parallelograms. 16 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.