Chapter 4 Foldable
Scalene All sides have a different length (measure).
IsoscelesAt least two of the sides have the same measure.
EquilateralAll three sides have the same measure
Equiangular All three angles are equal
RightOne angle is a right angle
and the other two are acute
ObtuseOne angle is greater than 90°
andthe other two are acute
AcuteAll three angles are less than 90°
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Side-Side-Side
SSSCongruence Postulate
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Side-Angle-Side
S-A-S
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
SAS
Angle-Side-Angle
A-S-A
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
A-S-A
Angle-Angle-Side
A-A-S
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
A-A-S
Hypotenuse-Leg
HL
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
Base Angle TheoremIf two sides of a triangle are congruent, then the
opposite angles are congruent.
Converseof
Base Angle Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
,
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Mid-segmentof a
Triangle
The mid-segment of a triangle is half the length of the base.
TriangleInequalities
5.10
If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
so, Triangle
Inequalities
Theorem 5.11
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. 54-
then, Triangle
Inequalities
Theorem 5.11The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
3+7 > 9 10 > 9
A
C
B7
9
3
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Inequalities in
2 Triangles
5.6
Hinge Theorem
“SAS”
If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.
WX > ST
Converse of theHinge Theorem
If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
E
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Ratios and Proportions Chapter 6
Ratios Ratio of a to b
When simplifying rations: the same unit they have to be simplified denominators CANNOT be zero
or a : b
ProportionsAn equation that equates two ratios
or
Properties
of Proportions
Cross Product
if
Reciprocals
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AA ~ Two angles are corresponding and to two angles in another triangle.
~
SSS ~ All three pairs of corresponding sides of two triangles are proportional.
SSS Similarity
~
SAS ~Two pairs of corresponding sides are proportional AND the included angle is congruent. ~
A
B
C
D
E
F
A
B
C D
E
F
Sine of
or
or
or
SOH CAH TOA
SOH CAH TOA SOH CAH TOA
J.Haugh\X Drive: Geometry Word Wall/Foldable: N. Shildneck Lecture Notes 2018
J.Haugh\X Drive: Geometry Word Wall/Foldable: N. Shildneck Lecture Notes 2018
