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 Δ 𝐵𝐺𝐸 ≅ Δ .𝐸𝐷𝐶

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