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Geometry - Chapter 4
Tehachapi High School Geometry Book
25
Mathematics
10th Grade
11/29/2012

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Term
Congruent
Definition
When two figures have the same size and shape.
Pg. 117
Term
Corresponding
Parts
Definition
When two shapes are ≅, then each < and side of one shape with correspond to an < and side of the other shape.
Pg. 117 - 118
Term
CPCT
Definition
Corresponding parts of ≅ ∆s are ≅
Used after a polygon is shown ≅ to another polygon.
Pg. 118
Term
SSS Postulate
Definition
Side Side Side Postulate
If three sides of one ∆ are ≅ to three sides of another ∆ then the ∆s are ≅
Pg. 122
Term
SAS Postulate
Definition
Side Angle Side Psotulate
If two sides and the included < of one ∆ are ≅ to two sides and the included < of anther ∆, then the ∆s are ≅
Pg. 122
Term
ASA Postulate
Definition
Angle Side Angle Postulate
If two <s and the included side of one ∆ are ≅ to two <s and the included side of anther ∆, then the ∆s are ≅
Pg. 123
Term
A line and a plane are ┴ IF
Definition
If and Only If they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection.
Pg. 128
Term
How to Prove Segments or <s ≅
Definition
1. Identify two ∆s in which the two segments or <s are corresponding parts.
2. Prove that the triangles are ≅
3. State that the two parts are ≅, using CPCT
Pg. 129
Term
Legs & Base
of an Isosceles ∆
Definition
*The legs of an isosceles ∆ are the ≅ sides.
*The base is the third side.
*The <s along the base are called base <s
*The < opp. the base is the vertex angle.
Pg. 134
Term
Isosceles ∆ Theorem
Definition
If two sides of a ∆ are ≅, then the <s opposite those sides are ≅.
Pg. 135
Term
Corollary 1, 2, & 3
of Isosceles ∆ Theorem
Definition
1. An equilateral ∆ is also equiangluar
2. An equilateral ∆ has three 60⁰ <
3. The bisector of the vertex < of an isosceles ∆ is ┴ to the base at its midpoint.
Pg. 135
Term
Theorem 4-2
Converse of Isosceles ∆ Theorem
Definition
If two <s of a ∆ are ≅, then the sides opposite those <s are ≅
Pg. 136
Term
Corollary 1
of Theorem 4-2
Definition
An equiangluar ∆ is also equilateral
Pg. 136
Term
AAS Theorem
Definition
Angle Angle Side Theorem
If two <s and a non-included side of one ∆ are ≅ to the corresponding parts of anther ∆, then the ∆s are ≅
Pg. 140
Term
Hypotenuse & Legs
of a Right ∆
Definition
Hypotenuse (hyp.)- the side opposite the right <
Legs - are the other two side or the ┴ sides
Pg. 141
Term
HL Theorem
Definition
Hypotenuse Leg Theorem
If the hypotenuse and a leg of one right ∆ are ≅ to the corresponding parts of another ∆, then the ∆s are ≅
Pg. 141
Term
Ways to Prove two ∆s ≅
Definition
All ∆: SSS SAS ASA AAS

Right ∆: HL
Pg. 141
Term
Median
Definition
A segment from a vertex to the midpoint of the opposite side.
Pg. 152
Term
Altitude
Definition
A ┴ segment from a vertex to the line that contains the opposite side Pg. 152
*Acute ∆s have all three altitudes inside the ∆
*Right ∆s have two altitudes as legs and the other inside the ∆
*Obtuse ∆s have two altitudes outside and one inside the ∆
Term
Perpendicular
Bisector
Definition
A segment that is ┴ to another segment at its midpoint
*The segment is both the altitude and median
Pg. 153
Term
Theorem 4-5
Starting with perp. bis
Definition
If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.
Pg. 153
Term
Theorem 4-6
Starting with point equidistant from endpts.
Definition
If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
Pg. 153
Term
Distance From
a Point to a Line
Definition
The length of the ┴ segment from the point to the line or plane.
*Important for theorem 4-7 and 4-8
Pg. 154
Term
Theorem 4-7
Starting with < bis.
Definition
If a point lies on the bisector of an <, then the point is equidistant from the sides of the <.
Pg. 154
Term
Theorem 4-8
Starting with pt. equidistant from sides of an <
Definition
If a point is equidistant from the sides of an <, then the point lies on the bisector of the <.
Pg. 154
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