The Case of the Missing Diagram

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Chapter 4.2

• The Case of the Missing Diagram

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• Objective After studying this section, you will
  be able to organize the information in, and draw
  diagrams for, problems presented in words.

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Set up a proof of the statement If two
altitudes of a triangle are congruent, then the
triangle is isosceles.

• Draw the shape, label everything.
• The if part of the statement is the given.
• The then part of the statement is the prove.
• Write the givens and what you want to prove.

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A

1. Draw a diagram to show two altitudes in a
   triangle. Label everything.
2. Write your given statements.
3. Write your prove statement.

E
B
D
C
Given BD CE are altitudes to AC AD of
ACD. BD ? CE. Prove ACD is isosceles.
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NOTICE!!!

• You can label everything on a diagram to help you
  make the proof.

Some problems you only have to draw, label, write
the givens and what to prove. Others you also
have to prove.
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Remember If.then. Sometimes you will see these
in reverse. The medians of a triangle are
congruent if the triangle is equilateral.

1. Draw the diagram.
2. Write down the givens you need.
3. What do you need to prove?

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X

1. Draw a diagram to show the medians in an
   equilateral triangle. Label everything.
2. Write your given statements.
3. Write your prove statement.

R
P
Y
Z
Q
Given XYZ is equilateral.PZ, RY, and QX are
medians. Prove PZ ? RY ? QX
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One more time. Try this one! If each pair of
opposite sides of a four-sided figure are
congruent, then the segments joining opposite
vertices bisect each other.

1. Draw
2. Write Given
3. Write Prove
4. Write proof

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A
B
E
C
D
Given AB ? CD AD ? BC Prove AC bisects
BD BD bisects AC
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? ABC ? ? CDA by SSS, and thus, ltBAC ? ltDCA. ?
BAD ? ? DCB by SSS, and thus, ltABD ? ltCDB. Thus
? ABE ? ? CDE by ASA, and then AE ? EC and DE ?
EB.