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Vertical Angles Theorem: When two lines cross or intersect, the angles that are mirrored are the same measure.The two intersecting line segments form four angles and the sum of two angles that form a straight line is 180° because of the definition of supplementary angles. Angle 1 + Angle 2 = 180°. Angles 2 and 3 also form a straight line, by definition of supplementary angles Angle 3 + Angle 4 = 180°. The sum of angles 1 and 2 are 180° and the sum of angles 3 and 4 is 180°, these would be equal to each other because of the Transitive property of Equality, Angles 1 and 2 is equal to the sum of angles 3 and 4. Next we would use the Subtraction Property of Equality angle 4 can be subtracted from both sides of the equation to prove that angle 1 and 3 are equal.
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Prove that the sides opposite the congruent base angles of a triangle are congruent. Be sure to create and name the appropriate geometric figures.
Isosceles Triangle Theorem: If two sides of a triangle are congruent then the angles opposite of those sides are congruent. So the two base angles are equal, but base angles aren't always the bottom of a triangle, these angles are adjacent to the unequal side of the triangle and an isosceles triangle is where all three sides are equal (equilateral triangle).
Let's say we have a triangle with ABC, AB ≅ BC and Angle C ≅ Angle A.
You can use the Reflective Property of Equality, SAS postulate, a straightedge, and compass to prove the isosceles triangle theorem.