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23 Cards in this Set
- Front
- Back
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Theorem 3-5
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If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
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Theorem 3-6
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If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
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Theorem 3-6 cont.
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The sum of the lengths of any two sides of a triangle is greater than the third side.
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Can a triangle have sides with 2, 3, and 4?
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yes, it can be a triangle
2+3 >4 2+4>3 3+4>2 |
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Can a triangle have sides with 3, 5, and 9?
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No, this cannot be a triangle
3+5>9 not true 3+9.5 true 5+9>3 true |
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PROOFs
Definition of a Linear Pair |
m<A + m<B = 180
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Substitution Property of equality
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m<A + 34 = 180
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Subtraction property of equality
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m<A = 146
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Angle Addition Postulate
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2 angles on one triangle = 2 angles on another triangle
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Congruent Polygons
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when all their corresponding parts (sides and angles) are congruent
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Congruent Triangles
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If two triangles are congruent then the corresponding sides and angles must be congruent. (biconditional statement)
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CONVERSE of congruent triangles
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If all the corresponding parts of two triangles are congruent, then the triangles are congruent.
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Triangle Congruency Postulates.
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three postulates and one theorem that prove that two triangles are congruent.
SSS SAS ASA |
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3-1 Side Side Side
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If 3 sides of one triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent.
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3-2 Side Angle Side
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If two sides and the included angle of one triangle are congruent to the corresponding sides and angle of a second triangle, then the triangles are congruent.
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Triangle Congruency Theorem
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If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
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Triangle Sum Theorem
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sum of the measures of the angle in a triangle =180
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Angle Angle Side
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If two angles and a non common side of one triangle are congruent to the corresponding angles and side of a second triangle, then the triangles are congruent.
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Segment AC = Segment AC
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Reflective (mirrors) Property of Equality
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CPCTC Theorem
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If two triangles are congruent, then all corresponding parts (SIDES and ANGLES) are congruent.
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Pythagorean Theorem
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In a right triangle, the sum of the square of each leg of the triangle is equal to the square of te hypotenuse. c^2= a^2 + b^2
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LL Theorem (Leg-Leg)
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If the legs of one right triangle are congruent tothe corresponding legs of another right triangle, then the triangles are congruent.
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HL Theorem (Hypotenuse -Leg)
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If the hypotenuse and a leg of one right triangle are congruent to the hypothenuse and leg of another right triangle, the triangles are congruent.
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