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Geometry: Theorems

Problems

Theorems for Other Polygons

Theorems for Angles and Circles

Problem : Square ABCD has diagonals that intersect at point E. How do you know that triangles AEC and DEB are congruent?

The diagonals bisect each other. Therefore, segments AE and DE are congruent, and segments EC and EB are congruent. The vertical angles AEC and DEB are congruent. Therefore, by SAS, triangles AEC and DEB are congruent.

Problem : Quadrilateral ABCD is a rhombus with diagonals that intersect at point E. Given angle ABE = 30 degrees and segment AD = 5, what is the area of triangle EBC?

3.125 times the square root of three.

Problem : What is the relationship between an upper base angle and a lower base angle of an isosceles trapezoid?

They are supplementary.

Problem : A midsegment connects the midpoints of the legs of an isosceles triangle. What is the most specific name by which the quadrilateral created can be called?

An isosceles trapezoid

Problem : The endpoints of a segment and a point on the perpendicular bisector of that segment are the three vertices of a triangle. What kind of triangle must it be?

An isosceles triangle

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