proofs math 2
DESCRIPTION
Proofs math 2. BE and CD intersect at A. Prove:TRANSCRIPT
![Page 1: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/1.jpg)
Geometry
Math 2
![Page 2: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/2.jpg)
![Page 3: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/3.jpg)
![Page 4: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/4.jpg)
![Page 5: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/5.jpg)
![Page 6: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/6.jpg)
![Page 7: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/7.jpg)
Proofs
![Page 8: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/8.jpg)
Lines and Angles Proofs
![Page 9: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/9.jpg)
BE and CD intersect at A. Prove: <BAD = < CAE ( in other words prove the vertical angle theorem)
![Page 10: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/10.jpg)
• Given that the lines are parallel and <2 = <6 • Prove <4 = <6 (alternate interior < theorem)
![Page 11: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/11.jpg)
• 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.
![Page 12: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/12.jpg)
Triangle Proofs
![Page 13: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/13.jpg)
Prove the angles of a triangle sum to 180
• 1. Draw a triangle
![Page 14: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/14.jpg)
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.
![Page 15: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/15.jpg)
![Page 16: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/16.jpg)
![Page 17: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/17.jpg)
Given that quadrilateral ADEG is a rectangle and ED bisects BC .
Prove Δ 𝐵𝐺𝐸 ≅ Δ .𝐸𝐷𝐶
![Page 18: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/18.jpg)
![Page 19: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/19.jpg)
![Page 20: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/20.jpg)
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)
![Page 21: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/21.jpg)
Practice Quad Properties
• KUTA
![Page 22: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/22.jpg)
![Page 23: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/23.jpg)
Rhombus
![Page 24: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/24.jpg)
Rectangles
![Page 25: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/25.jpg)
![Page 26: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/26.jpg)
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)
![Page 27: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/27.jpg)
• 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)
![Page 28: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/28.jpg)
• 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)
![Page 29: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/29.jpg)
• 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)
![Page 30: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/30.jpg)
![Page 31: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/31.jpg)
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)
![Page 32: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/32.jpg)
Given that ABCD is a parallelogram with <1 = <2
Prove: ABCD is a rhombus (prove the property that bisected opposite angles create a rhombus)
![Page 33: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/33.jpg)
Given that ABCD is a parallelogram with corners that each are 90 degrees.Prove: AC = BD (prove the property that rectangles have congruent diagonals)
![Page 34: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/34.jpg)
![Page 35: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/35.jpg)
Constructions and their Proofs
![Page 36: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/36.jpg)
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
![Page 37: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/37.jpg)
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.
![Page 38: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/38.jpg)
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
![Page 39: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/39.jpg)
![Page 40: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/40.jpg)
Similar Triangle Proofs
![Page 41: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/41.jpg)
Show that the segment joining the midpoints of the sides of a triangle is parallel to the base and ½ the bases length
![Page 42: Proofs math 2](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568150b0550346895dbecd36/html5/thumbnails/42.jpg)
Prove the two triangles similar