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Transcript of Day 7 agenda Go over homework- 5 min Take up for an effort grade Warm-up- 10 min 5.5 notes- 50 min...
![Page 1: Day 7 agenda Go over homework- 5 min Take up for an effort grade Warm-up- 10 min 5.5 notes- 50 min Start homework- 20 min Make sure students have time.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfeb1a28abf838cb7a6b/html5/thumbnails/1.jpg)
Warm-Up:EOC Review
What is the negation of x ≤ 10?
A) x ≤ 10B) –x ≤ 10C) –x > 10D) x > 10
What is the inverse of p q?
A) q pB) ~q ~pC) p qD) ~p ~q
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Inequalities in Triangles5.5
1. Use inequalities involving angles of triangles.
2. To use inequalities involving sides of triangles.
Today’s GoalsBy the end of class today, YOU should be able to…
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Comparison Property of Inequality
If a = b + c and c > 0, then a > b.
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Proof of the Comparison Property of Inequality
Given: a = b + c, and c > 0
Prove: a > b
Statement 1: c > 0 Given
Statement 2: b + c > b + 0
Addition Property of Inequality
Statement 3: b + c > b
Simplify
Statement 5: a > b Substitute a for b + c in Statement 3
Statement 4: a = b + c Given
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Corollary to the Triangle Exterior Angle Theorem
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.m<1 > m<2 and m<1 > m<3
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Theorem 5-10
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.If XZ > XY, then m<Y > m<Z.
![Page 7: Day 7 agenda Go over homework- 5 min Take up for an effort grade Warm-up- 10 min 5.5 notes- 50 min Start homework- 20 min Make sure students have time.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfeb1a28abf838cb7a6b/html5/thumbnails/7.jpg)
Theorem 5-11
If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. If m<A > m<B, then BC > AC.
![Page 8: Day 7 agenda Go over homework- 5 min Take up for an effort grade Warm-up- 10 min 5.5 notes- 50 min Start homework- 20 min Make sure students have time.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfeb1a28abf838cb7a6b/html5/thumbnails/8.jpg)
Ex.1: Using Theorem 5-11
In TUV, which side is shortest?
![Page 9: Day 7 agenda Go over homework- 5 min Take up for an effort grade Warm-up- 10 min 5.5 notes- 50 min Start homework- 20 min Make sure students have time.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfeb1a28abf838cb7a6b/html5/thumbnails/9.jpg)
Ex.1: Solution
By the Triangle Angle-Sum Theorem, m<T = 60. The smallest angle in TUV is U. It follows, by Theorem 5-11, that the shortest side is TV.
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You Try…
Which side is shortest?
Which side is longest?
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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.XY + YZ > XZYZ + ZX > YXZX + XY > ZY
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Ex.2: Using the Triangle Inequality Theorem
Can a triangle have sides with the given lengths?
3ft, 7ft, 8ft
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Ex.2: Solution
3 + 7 > 88 + 7 > 33 + 8 > 7
Yes, the sum of any two lengths is greater than the third length
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You Try…
Can a triangle have sides with the given lengths?
3ft, 6 ft, 10 ft
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Ex.3: Using the Triangle Inequality Theorem
A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.
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Ex.3: Solution
Let x represent the length of the third side.
8 + 10 > xx < 18
x + 10 > 8
x > -2
x + 8 > 10
x > 2
The third side must be longer than 2 cm and shorter than 18 cm.
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You Try…
A triangle has sides of lengths 7 in and 4 in. Describe the lengths possible for the third side.
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Homework
Page 276 #s 1, 6, 7, 14, 17, 20, 24, 25
Page 277 # 34The assignment can also be found
at:•http://www.pearsonsuccessnet.com/sn
papp/iText/products/0-13-037878-X/Ch05/05-05/PH_Geom_ch05-05_Ex.pdf