At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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.
Not the answer you are looking for? Search for more explanations.
Thank you, could you check this one too?
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.