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28 Cards in this Set
- Front
- Back
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Two triangles are congruent
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If the six parts of the first triangle are congruent to the six corresponding parts of the second triangle.
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Postulate 12
Side-side-side (sss) |
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent
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Postulate 13
Side-angle-side (SAS) |
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 triangles are congruent
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Identity
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Is the reason we site when verifying that a line segment or an angle is congruent to itself; also known as reflex property of congruence he |
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Postulate 14
Angle- side- angle (ASA) |
If two angles and the included side of one angle are congruent to two angles of an included side of a second triangle, then the triangles are congruent
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Theorem 3.1.1
Angle- angle- side (AAS) |
If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the triangles are congruent
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CPCTC
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Corresponding parts of a congruent triangles are congruent
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Theorem 3.2.1
Hypotenuse leg (HL) |
If the hypotenuse and a leg from one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent
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Theorem
Pythagorean |
The square of the measure of a hypotenuse is equal to the sum of the square of the measure of the legs
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Median
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Of a triangle is a line segment ( or line or Ray) that joins the vertex to the midpoint of the opposite side
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Altitude
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Of a triangle is a line segment drawn from the vertex to the opposite side such as that it is perpendicular to the opposite side, or an extension of the opposite side.
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Theorem 3.3.1
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Corresponding altitude of congruent triangles are congruent.
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Theorem 3.3.2
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The bisector of ever text angle of an I saucily's triangle separates the triangle into two congruent triangles.
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Theorem 3.3.3
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If two sides of a triangle are congruent, then the angles opposite of the sides are congruent.
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Theorem 3.3.4
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If two angles of a triangle are congruent, then the op. cit. sides of these angles are congruent.
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Perimeter
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Of a polygon is the sum of the links of all sides of the polygon
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A is less then B (a<b)
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If and only if there exist a positive number P for which a+p= b
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A is greater then b (a>b)
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If and only if B <a
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The trichotomy property |
For any a, B , only one of the following can be true ab
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Addition property inequality
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If b<a and c<d, the b+c<a+d
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Lemma 1 |
If B is between eight and a C on line segment AC , Then AB< AC and BC<AC
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Lemma 2
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Lemma 3
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Lemma 4
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theorem |
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Theorem
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Corollary
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6 |
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Theorem
The triangle inequality |
7 |
