Factor each polynomial.

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• Factor each polynomial.
• 1.
• 2.
• 3.
• 4.

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Homework Answers

• 13) Assume
• 16) Assume a median of an isosceles triangle is
  not an altitude
• 22) Step 1 Assume l m
• Step 2 by the corr. lts
  postulate, so mlt1mlt2 (def congruence)
  CONTRADICTION
• Step 3 Our assumption led to a contradiction,
  hence our assumption must be false. Therefore, l
  m

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HW Answers (contd)

• 26) Step 1 Assume BCltAC
• Step 2 mltAltmltB (angle side inequality)
• CONTRADICTION
• Step 3 Since our assumption led to a
  contradiction, our assumption must be false.
  Therefore, BC gt AC
• 37) ltP 38) ltN

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Statements Reasons
CD is an lt bisector, CD is an altitude ltACD is congruent to ltBCD CD is perpendicular to AB ltCDA ltCDB are rt lts ltCDA is conruent to ltCDB CD is congruent to CD Triangle ACD is congruent to Traingle BCD AC is congruent to BC Triangle ACB is isosc. Given Def lt bisector Def altitude Def perpendicular All rt lts are congruent Reflexive prop ASA CPCTC Def Isosc.
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Statements Reasons
QT is a median, Triangle QRS is isosceles with base RS T is a midpoint of SR RT is congruent to ST QR is congruent to QS QT is congruent to QT Triangle QRT is congruent to Triangle QST ltSQT is congruent to ltRQT QT bisects ltSQR Given Def median Midpt Thm Def isosc. Reflexive Prop SSS CPCTC Def lt bisector
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Statements Reasons
Triangle QRS is congruent to Triangle UTV, QW bisects ltRQS and UX bisects ltTUV ltRQS is congruent to ltTUV, QR is congruent to UT, ltR is congruent to ltT ltRQW is congruent to ltSQW, ltTUX is congruent to ltVUX mltRQW mltSQW, mltTUX mltVUX MltRQSmltRQWmltSQW, mltTUVmltTUX mltVUX MltRQWmltSQWmltTUX mltVUX 2mltRQW 2mltTUX mltRQW mltTUX ltRQW is congruent to ltTUX Triangle RQW is congruent to Triangle TUX QW is congruent to UX Given CPCTC Def lt bisector Def congruence Angle Addition Post Substitution Substitution/Combine Like terms Division Def congruence ASA CPCTC
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Human Triangles

• Measure each piece of string you were given.
• Use the pieces of string given to you to make a
  triangle (you must use the entire piece).
• Record your findings / Discussion

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Conclusion?
String Lengths Triangle?







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• Triangle Inequality Theorem The sum of the
  lengths of any two sides of a triangle is greater
  than the length of the third side.
• Picture
• AB BC gt AC
• BC AC gt AB
• AC AB gt BC

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• Theorem The perpendicular segment from a point
  to a line is the shortest segment from the point
  to the line.
• Picture
• Corollary The perpendicular segment from a point
  to a plane is the shortest segment from the point
  to a plane.

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Example 4-1a
Answer Because the sum of two measures is not
greater than the length of the third side, the
sides cannot form a triangle.
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Example 2
Two sides of a triangle are 4 and 13. Find the
range of the third side of the triangle.
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Example 4-1b
Determine whether the measures 6.8, 7.2, and 5.1
can be lengths of the sides of a triangle.
Check each inequality.
Answer All of the inequalities are true, so 6.8,
7.2, and 5.1 can be the lengths of the sides of a
triangle.
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Example 4-1c
Determine whether the given measures can be
lengths of the sides of a triangle. a. 6, 9,
16 b. 14, 16, 27
Answer no
Answer yes
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Example 4-2a
A 7 B 9 C 11 D 13
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Example 4-2a
Read the Test Item
You need to determine which value is not valid.
Solve the Test Item
Solve each inequality to determine the range of
values for PR.
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Example 4-2a
Graph the inequalities on the same number line.
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Example 4-2a
Examine the answer choices. The only value that
does not satisfy the compound inequality is 13
since 13 is greater than 12.4. Thus, the answer
is choice D.
Answer D
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Example 4-2b
A 4 B 9 C 12 D 16
Answer D
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Example 4-3a
Prove KJ lt KH
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Example 4-3a
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Example 4-3b
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Example 4-3b
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Example 4-3b
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display the answers.
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