Warm-Up

1
Warm-Up

1. What does it mean for two triangles to be
   congruent?

• If a contractor was building a house, how could
  she or he check to see if all of the roof
  trusses, which are triangles, were identical?

2
Warm-Up

1. What does it mean for two triangles to be
   congruent?

• If a contractor was building a house, how could
  she or he check to see if all of the roof
  trusses, which are triangles, were identical?

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4.2 Apply Congruence and Triangles4.3 Prove
Triangles Congruent by SSS

• Objectives
• To define congruent triangles
• To write a congruent statement
• To prove triangles congruent by SSS

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Congruent Polygons
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Congruent Triangles (CPCTC)

• Two triangles are congruent triangles if and only
  if the corresponding parts of those congruent
  triangles are congruent.

• Corresponding sides are congruent
• Corresponding angles are congruent

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Congruence Statement

• When naming two congruent triangles, order is
  very important.

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Example 1

• Write a congruence statement for the congruent
  triangles below.

Pay Attention to marking
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Example 2

• Which polygon is congruent to ABCDE?
• ABCDE ? -?-

QLMNP
9
Example 3

• Locate points I and S so that BLUE ? FISH.
• HINT use distance an slope to locate the new
  points

S
I
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Properties of Congruent Triangles
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Example 4

• What is the relationship between ltC and ltF?

They are corresponding and congruent
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Third Angle Theorem

• If two angles of one triangle are congruent to
  two angles of another triangle, then the third
  angles are also congruent.

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Example 5

• Now back to the subject of roof trusses. Would
  it be necessary for the manufacturer of a set of
  trusses to check that all the corresponding
  angles were congruent as well as the sides?

Answer and explain in your notebook
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Example 5

• In other words, is it sufficient that the pieces
  of wood (the sides of each triangle) are all the
  same length?

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Copying a Segment

• Were going to try making two congruent triangles
  by simply copying the three sides using only a
  compass and a straightedge. First, lets learn
  how to copy a segment.

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Copying a Segment

• Draw segment AB.

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Copying a Segment

1. Draw a line with point A on one end.

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Copying a Segment

1. Put point of compass on A and the pencil on B.
   Make a small arc.

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Copying a Segment

1. Put point of compass on A and use the compass
   setting from Step 3 to make an arc that
   intersects the line. This is B.

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Copying a Segment

• Click on the button to watch a video of the
  construction.

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Investigation 1

• Now apply the construction for copying a segment
  to copy the three sides of a triangle.

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Investigation 1

1. Use your straight edge to construct a triangle.
2. Now draw a line with A on one end.

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Investigation 1

1. Copy segment AB onto your line to make AB.

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Investigation 1

1. Put point of compass on A and pencil on C. Copy
   this distance from A.

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Investigation 1

1. Put point of compass on B and pencil on C. Copy
   this distance from B. This is C

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Investigation 1

1. Finish your new triangle by drawing segments AC
   and BC.

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Investigation 1

1. Copy the original triangle ABC onto a piece of
   patty paper. Compare this triangle to triangle
   ABC. Are they congruent?

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Side-Side-Side Congruence Postulate

• SSS Congruence Postulate
• If the three sides of one triangle are congruent
  to the three sides of another triangle, then the
  two triangles are congruent.

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SSS Congruence Postulate
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Example 6

• Decide whether the triangles are congruent.
  Explain your reasoning.

Answer in your notebook
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Example 7
32
Example 8

• Explain why the bench with the diagonal support
  is stable, while the one without the support can
  collapse.

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Assignment

• P. 228-231 1-3, 11-16,19, 20, 26, 28, 33, 34
• P. 236-239 5-7, 9, 18,19, 28, 29, 30, 31, 32
• Challenge Problems (Pick 2 Proofs)