Term
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Definition
When two figures have the same size and shape.
Pg. 117 |
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Term
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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 |
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Term
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Definition
Corresponding parts of ≅ ∆s are ≅
Used after a polygon is shown ≅ to another polygon.
Pg. 118 |
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Term
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Definition
Side Side Side Postulate
If three sides of one ∆ are ≅ to three sides of another ∆ then the ∆s are ≅
Pg. 122 |
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Term
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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 |
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Term
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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 |
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Term
| A line and a plane are ┴ IF |
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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 |
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Term
| How to Prove Segments or <s ≅ |
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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 |
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Term
Legs & Base
of an Isosceles ∆ |
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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 |
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Term
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Definition
If two sides of a ∆ are ≅, then the <s opposite those sides are ≅.
Pg. 135 |
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Term
Corollary 1, 2, & 3
of Isosceles ∆ Theorem |
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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 |
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Term
Theorem 4-2
Converse of Isosceles ∆ Theorem |
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Definition
If two <s of a ∆ are ≅, then the sides opposite those <s are ≅
Pg. 136 |
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Term
Corollary 1
of Theorem 4-2 |
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Definition
An equiangluar ∆ is also equilateral
Pg. 136 |
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Term
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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 |
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Term
Hypotenuse & Legs
of a Right ∆ |
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Definition
Hypotenuse (hyp.)- the side opposite the right <
Legs - are the other two side or the ┴ sides
Pg. 141 |
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Term
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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 |
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Term
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Definition
All ∆: SSS SAS ASA AAS
Right ∆: HL
Pg. 141 |
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Term
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Definition
A segment from a vertex to the midpoint of the opposite side.
Pg. 152 |
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Term
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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 ∆ |
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Term
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Definition
A segment that is ┴ to another segment at its midpoint
*The segment is both the altitude and median
Pg. 153 |
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Term
Theorem 4-5
Starting with perp. bis |
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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 |
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Term
Theorem 4-6
Starting with point equidistant from endpts. |
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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 |
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Term
Distance From
a Point to a Line |
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Definition
The length of the ┴ segment from the point to the line or plane.
*Important for theorem 4-7 and 4-8
Pg. 154 |
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Term
Theorem 4-7
Starting with < bis. |
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Definition
If a point lies on the bisector of an <, then the point is equidistant from the sides of the <.
Pg. 154 |
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Term
Theorem 4-8
Starting with pt. equidistant from sides of an < |
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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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