Download Proofs math 2 - Sage Middle School

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
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•
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•
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