Download 8.7 Congruent Triangles and Properties of

Geometry
CHAPTER
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Basic Geometric Figures
Perimeter
Area
Circles
Volume and Surface Area
Relationships Between Angle Measures
Congruent Triangles and Properties of
Parallelograms
8.8 Similar Triangles
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 2
8.7
Congruent Triangles and Properties of
Parallelograms
OBJECTIVES
a Identify the corresponding parts of congruent
triangles and show why triangles are congruent using
SAS, SSS, and ASA.
b Use properties of parallelograms to find lengths of
sides and measures of angles of parallelograms.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 3
8.7
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles
a and show why triangles are congruent using SAS, SSS,
and ASA.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 4
8.7
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles
a and show why triangles are congruent using SAS, SSS,
and ASA.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 5
8.7
Congruent Triangles and Properties of
Parallelograms
CONGRUENT TRIANGLES
Two triangles are congruent if and only if their vertices
can be matched so that the corresponding angles and
sides are congruent.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 6
8.7
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles
a and show why triangles are congruent using SAS, SSS,
and ASA.
The corresponding sides and angles of two congruent
triangles are called corresponding parts of congruent
triangles. Corresponding parts of congruent triangles are
always congruent.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 7
8.7
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles
a and show why triangles are congruent using SAS, SSS,
and ASA.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 8
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 3
Suppose that
corresponding parts?
What are the congruent
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 9
8.7
Congruent Triangles and Properties of
Parallelograms
THE SIDE–ANGLE–SIDE (SAS) PROPERTY
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.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 10
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 5
Which pairs of triangles on the next slide are congruent
by the SAS property?
Pairs (b) and (c) are congruent by the SAS property.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 11
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 5
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 12
8.7
Congruent Triangles and Properties of
Parallelograms
THE SIDE–SIDE–SIDE (SSS) PROPERTY
If three sides of one triangle are congruent to three
sides of another triangle, then the triangles are
congruent.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 13
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 6
Which pairs of triangles are congruent by the SSS property?
Pairs (b) and (d) are congruent by the SSS property.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 14
8.7
Congruent Triangles and Properties of
Parallelograms
THE ANGLE–SIDE–ANGLE (ASA) PROPERTY
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.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 15
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 7
Which pairs of triangles are congruent by the ASA
property?
Pairs (b) and (c) are congruent by the ASA property.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 16
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 13
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 17
8.7
a
Congruent Triangles and Properties of
Parallelograms
Identify the corresponding parts of congruent triangles and
show why triangles are congruent using SAS, SSS, and ASA.
EXAMPLE 14
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 18
8.7
Congruent Triangles and Properties of
Parallelograms
PROPERTIES OF PARALLELOGRAMS
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.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 19
8.7
Congruent Triangles and Properties of
Parallelograms
Use properties of parallelograms to find lengths of
b
sides and measures of angles of parallelograms.
EXAMPLE 16
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 20