Geometry and Art and Geometry and Time Part 2, Geometry and Time.
Geometry
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Geometry Geometry 6.5 Inequalities for Two 6.5 Inequalities for Two Triangles Triangles
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Geometry. 6.5 Inequalities for Two Triangles. SAS Inequality Theorem. If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle - PowerPoint PPT Presentation
Transcript of Geometry
GeometryGeometry
6.5 Inequalities for Two Triangles6.5 Inequalities for Two Triangles
SAS Inequality TheoremSAS Inequality Theorem If two sides of one triangle are congruent to two sides of anotherIf two sides of one triangle are congruent to two sides of another
triangle, but the included angle of the first triangle is larger than thetriangle, but the included angle of the first triangle is larger than the
included angle of the second, then the third side of the first triangle included angle of the second, then the third side of the first triangle
is longer than the third side of the second triangle.is longer than the third side of the second triangle.
Imagine a stick in the crocodile’s mouth.
What would the crocodile do to fit a longerstick in her jaws?
She cannot lengthen her jaws, they are the congruent side of the triangle.
She can, however, change the included angleof the two sides of her jaw, therefore making the side opposite that angle bigger.
small
small
BIG
BIG
Therefore, the stick (the third side) would be longer.
SSS Inequality TheoremSSS Inequality Theorem
If two sides of one triangle are congruent to two sides of another triangle, If two sides of one triangle are congruent to two sides of another triangle,
but the third side of the first triangle is larger than the third side of the second, but the third side of the first triangle is larger than the third side of the second,
then the included angle of the first triangle is larger than the included angle of then the included angle of the first triangle is larger than the included angle of
the second triangle.the second triangle.
BIG
BIG small
small
AB
C D 1 2
3.05
4.1
Examples: What can you deduce from the given information? What theorem applies?
1.
3.
mDCB > mABC
D is the midpoint of AC
m1 < m2
2.
AB CD
4.
A
B
CD
2 1
G
E
O
S
6
6
6
7
5. 6.
7. 8.
A
B
C
D 3x5x
6 7
1 2
6
6 6
6
6
8
A
3
B
A B
C
D
12 12
4243
Examples: What can you deduce from the given information? What theorem applies?
HWHW
P. 230-232P. 230-232 CE (#1-8) CE (#1-8) WE (#1-11)WE (#1-11)
What can you deduce from the given information? What can you deduce from the given information? Name the theorem that supports your answer.Name the theorem that supports your answer.
A D C
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BD is the midpoint of AC.
m 1 < m 2
7 7BIGsmall
smallBIG
ANSWER: AB < BC
By SAS Ineq. Thm.
GIVEN:
What can you deduce from the given information? What can you deduce from the given information? Name the theorem that supports your answer.THIS Name the theorem that supports your answer.THIS
SLIDE MAY BE INCORRECTSLIDE MAY BE INCORRECT
6
6
6
7
S
E
OG
ANSWER: m GSE < m SEO
By SSS Ineq. Thm.
BIG
small
small
BIG
77
What can you deduce from the given information? What can you deduce from the given information? Name the theorem that supports your answer.Name the theorem that supports your answer.
B A
C
AB = CD
m DCB > m ABC
7 7
GIVEN:
B
C
A
D
BIG
small
BIG
small
ANSWER: DB > AC
By SAS Ineq. Thm.
What can you deduce from the given information? What can you deduce from the given information? Name the theorem that supports your answer.Name the theorem that supports your answer.
A B
6
6
38
6 6
6
ANSWER: m A > m B
By SSS Ineq. Thm.
77
BIG
BIG small
small
What can you deduce from the given information? What can you deduce from the given information? Name the theorem that supports your answer.Name the theorem that supports your answer.
ANSWER: m 1 > m 2
By SSS Ineq. Thm. And Iso. Triangle Thm.
77
1 2
6 7 BIG
BIG
small
small
But how does that affect the measures of angles 1 and 2?
Let’s throw in some possible measurements!
100
80
50 50 40 40
A Few From the HWA Few From the HW
P. 230 #5 P. 230 #5 P. 231 #3P. 231 #3
