geometric proofs involving complementary and supplementary … · pom is a right angle por is...
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![Page 1: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/1.jpg)
Geometric Proofs Involving Complementary
and Supplementary Angles
October 18, 2010
![Page 2: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/2.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Warm - Up
![Page 3: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/3.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
![Page 4: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/4.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Given: TVK is a right angle.
Prove: 1 is complementary to 2.
![Page 5: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/5.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Given: TVK is a right angle.
Prove: 1 is complementary to 2.
Statements Reasons
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
TVK is a right angle. Given
Angle Addition Postulate
Substitution
Definition of Complementary s
m TVK = 90
1 + 2 = TVK
1 + 2 = 90
1 is complementary to 2.
A right angle measures 90
![Page 6: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/6.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Given: ABC is a straight angleProve: 1 is supplementary to 2.
1 2
A B C
![Page 7: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/7.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Given: ABC is a straight angleProve: 1 is supplementary to 2.
Statements Reasons
1. 1.
2. 2.
3. 3.
4. 4.
ABC is a straight angle Given
Definition of Linear Pairs
Linear Pairs form supplementary angles.
1 and 2 form a Linear pair
1 2
A B C
1 is supplementary to 2
Angle Addition Postulate1 + 2 = ABC
![Page 8: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/8.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
![Page 9: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/9.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
![Page 10: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/10.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Statements Reasons
1. 1. 1 is complementary to 2 given
2. Complements Theorem
3 is complementary to 2
2. 1 3
![Page 11: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/11.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
![Page 12: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/12.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
Given: 1 4 Prove: 2 3
Statements Reasons
1. 1 4 1. given
1 2 3 4
2. 1 and 2 form a Linear pair
2. Definition of Linear Pair
3 and 4 form a Linear pair
3. Linear Pairs form Supplementary angles.
3. 1 is suppl. to 23 is suppl. to 4
4. 2 3 4. Supplements Theorem
![Page 13: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/13.jpg)
SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems.
![Page 14: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/14.jpg)
Statements Reasons
1. 1. given
KMR POR
K
M O
PR
2. Definition of lines
5. RMO ROM
2. KMO and POM are right angles
3. KMO POM 3. All right Angles are
4.KMO - KMR POM - RMO
4. Subtraction Property (3, 1)
5. Substitution Property
6. ROM RMO 6. Symmetric Property
![Page 15: Geometric Proofs Involving Complementary and Supplementary … · POM is a right angle POR is compl. to ROM 5. KMR is compl. to RMO 5. Definition of Complementary s 3. KMO 90 3. Right](https://reader033.vdocuments.us/reader033/viewer/2022050315/5f77612a65d88a0b146a3e5e/html5/thumbnails/15.jpg)
Statements Reasons
2. KMO is a right angle 2. Definition of linesPOM is a right angle
POR is compl. to ROM
5. Definition of Complementary s5. KMR is compl. to RMO
3. Right s are to 903. KMO 90POM 90
4. KMR + RMO KMOPOR + ROM POM
4. Angle Addition Postulate
5. KMR + RMO 90POR + ROM 90
5. Substitution (3 into 4)
6. Complements Theorem
1. 1. given
KMR POR
K
M O
PR
6. ROM RMO