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Geometry Math 2 Proofs Lines and Angles Proofs BE and CD intersect at A. Prove: <BAD = < CAE ( in other words prove the vertical angle theorem) • Given that the lines are parallel and <2 = <6 • Prove <4 = <6 (alternate interior < theorem) • Given that the lines are parallel and <3 + <6 = 180 • Prove <2 = <6 (prove corresponding angle theorem) - You may not use alternate interior, consecutive interior, or alternate exterior thrms. Triangle Proofs Prove the angles of a triangle sum to 180 • 1. Draw a triangle Given that line l is the perpendicular bisector of line AB: Prove that any point on line l will be equidistant from the endpoints A and B. Given that quadrilateral ADEG is a rectangle and ED bisects BC . Prove Δ𝐵𝐺𝐸 ≅ Δ𝐸𝐷𝐶. Given that two legs of the triangle are congruent, Prove the angles opposite them are also congruent. (Prove that base angles of an isosceles triangle are congruent) Practice Quad Properties • KUTA Rhombus Rectangles Given that circle A and circle B are congruent 1. 1. Prove that ADBC is a rhombus 2. Prove that CP is perpendicular to AB (prove that this construction works every time) • Given that AB is parallel to CD and AD is parallel to BC • Prove: AB = CD and AD = BC (prove the property that opposite sides of a parallelogram are congruent) • Given that AB is parallel to CD and AB = CD • Prove that AE = EC and DE = EB (Prove the property that diagonals bisect each other in a parallelogram) • Given that AB is parallel to CD and AD is parallel to BC • Prove that <DAB = <BCD (Prove the property that opposite angles are congruent in a parallelogram) Given: ABCD is a parallelogram with AC perpendicular to BD Prove: ABCD is also a rhombus (Prove the property: perpendicular diagonals on a parallelogram make a rhombus) Given that ABCD is a parallelogram with <1 = <2 Prove: ABCD is a rhombus (prove the property that bisected opposite angles create a rhombus) Given that ABCD is a parallelogram with corners that each are 90 degrees. Prove: AC = BD (prove the property that rectangles have congruent diagonals) Constructions and their Proofs Create the following constructions • • • • Copy a line Copy an angle Create a perpendicular bisector Create a line parallel to a another line through a point • Construct a square • Inscribe a hexagon, equilateral triangle, and a right triangle Given: Circle A and circle B are congruent to each other. A and B are on the circumference of circle F. Prove FAC congruent to FBC. Given: Circle A and circle B are congruent to each other. A and B are on the circumference of circle F. Prove: <AFC congruent to <BFC (prove the construction of angle bisectors works Similar Triangle Proofs Show that the segment joining the midpoints of the sides of a triangle is parallel to the base and ½ the bases length Prove the two triangles similar