Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF...
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Transcript of Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF...
![Page 1: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/1.jpg)
Warm UpWarm Up
Given BCDF is a kiteBC = 3x + 4yCD = 20BF = 12FD = x + 2yFind the PERIMETER OF BCDF
Given BCDF is a kiteBC = 3x + 4yCD = 20BF = 12FD = x + 2yFind the PERIMETER OF BCDF
P = 2(12) + 2(20) = 64
![Page 2: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/2.jpg)
5.7 Proving that figures are special quadrilaterals
5.7 Proving that figures are special quadrilaterals
![Page 3: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/3.jpg)
Given: AB || CD <ABC <ADC
AB ADProve: ABCD is a rhombus
Given: AB || CD <ABC <ADC
AB ADProve: ABCD is a rhombus
B
D
C
A
![Page 4: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/4.jpg)
Proving a RhombusProving a RhombusFirst prove that it is a parallelogram then
one of the following
1. If a parallelogram contains a pair of consecutive sides that are congruent, then it is a rhombus (reverse of the definition).
2. If either diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus.
First prove that it is a parallelogram then one of the following
1. If a parallelogram contains a pair of consecutive sides that are congruent, then it is a rhombus (reverse of the definition).
2. If either diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus.
![Page 5: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/5.jpg)
Proving a rectangleProving a rectangle
First you must prove that the quadrilateral is a parallelogram and then prove one of the following conditions.
First you must prove that the quadrilateral is a parallelogram and then prove one of the following conditions.
![Page 6: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/6.jpg)
1. If a parallelogram contains at least one right angle, then it is a rectangle (reverse of the definition)
Or
2. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
1. If a parallelogram contains at least one right angle, then it is a rectangle (reverse of the definition)
Or
2. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
![Page 7: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/7.jpg)
You can also prove a quadrilateral is a rectangle without first showing that it is a parallelogram if you can prove that all four angles are right angles.
If all four angles are right angles, then it is a rectangle.
You can also prove a quadrilateral is a rectangle without first showing that it is a parallelogram if you can prove that all four angles are right angles.
If all four angles are right angles, then it is a rectangle.
![Page 8: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/8.jpg)
Proving a kiteProving a kite
1. If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it is a kite (reverse of the definition).
2. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then the quadrilateral is a kite.
1. If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it is a kite (reverse of the definition).
2. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then the quadrilateral is a kite.
![Page 9: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/9.jpg)
You can also prove a quadrilateral is a rhombus if the diagonals are perpendicular bisectors of each other, then the quadrilateral is a rhombus.
You can also prove a quadrilateral is a rhombus if the diagonals are perpendicular bisectors of each other, then the quadrilateral is a rhombus.
![Page 10: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/10.jpg)
Prove a squareProve a square
If a quadrilateral is both a rectangle and a rhombus, then it is a square (reverse of the definition).
If a quadrilateral is both a rectangle and a rhombus, then it is a square (reverse of the definition).
![Page 11: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/11.jpg)
Prove an isosceles trapezoidProve an isosceles trapezoid 1. If the nonparallel sides of a trapezoid are
congruent, then it is isosceles (reverse of the definition).
2. If the lower or upper base angles of a trapezoid are congruent, then it is isosceles.
3. If the diagonals of a trapezoid are congruent then it is isosceles.
1. If the nonparallel sides of a trapezoid are congruent, then it is isosceles (reverse of the definition).
2. If the lower or upper base angles of a trapezoid are congruent, then it is isosceles.
3. If the diagonals of a trapezoid are congruent then it is isosceles.
![Page 12: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/12.jpg)
Rectangle
![Page 13: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/13.jpg)
Kite
![Page 14: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/14.jpg)
Rhombus
![Page 15: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/15.jpg)
Square
![Page 16: Warm Up Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD = x + 2y Find the PERIMETER OF BCDF Given BCDF is a kite BC = 3x + 4y CD = 20 BF = 12 FD =](https://reader036.fdocuments.us/reader036/viewer/2022081811/5697c0131a28abf838cccdd1/html5/thumbnails/16.jpg)
Isosceles trapezoid