section 3.7 angle-side theorems
DESCRIPTION
Section 3.7 Angle-Side Theorems. By: Kellan Hirschler and Katherine Rosencrance. Theorem 20: If two sides of a triangle are congruent, the angles opposite the sides are congruent. Symbolic form: If , then (If sides, then angles). E. Given:. Conclusion:. A. T. - PowerPoint PPT PresentationTRANSCRIPT
BY: KELLAN HIRSCHLER AND KATHERINE ROSENCRANCE
Section 3.7 Angle-Side Theorems
Theorem 20: If two sides of a triangle are congruent, the angles opposite the sides are congruent. Symbolic form: If , then (If sides, then angles)
Given: E
A T
EA ETConclusion: A E
Theorem 21: If two angles of a triangle are congruent, the sides opposite the angles are congruent.Symbolic form: If , then (If angles, then sides)
Given: P
I E
I E
Conclusion: PI PE
Prove: PIK PGK
P
I GK
S R
1. IK KG 1. GivenI 2. G 2. Given
3. PI PG 3. If angles, then sides4. PIK PGK 4. SAS (1,2,3)
Theorem: If two sides of a triangle are not congruent, then the angles opposite them are not congruent and the larger angle is opposite the longer side.
Symbolic Form: If , then .
Longer
Larger
Shor
ter
Smaller
Theorem: If two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the longer side is opposite the larger angle.
Symbolic Form: If , then . Sh
orte
r Longer
SmallerLarger
2 ways to prove a triangle is isosceles:If , then is isosceles.
If , then is isosceles.
Equilateral triangle <=> Equiangular triangle
<=>
H
O R S E
Given: OHR EHS
OH HE
Prove: HR HS
S R1. OHR EHS 1. Given2. OH HE 2. Given
3. O H 3. If sides, then angles
4. OHR EHS 4. ASA (1,2,3)
5. HR HS 5. CPCTC
REVIEWO
W L
Given: OW OL
Conclusion: W L
R
O W
Given: O W Conclusion: RORW
K A T I
E
Given: KTAI
KEI is isos. with and KEIE
S R
Prove: KET IEA
1. AI KT 1. Given
KEI is isos. with
IE andKE
;
3. K I3. If the triangle is isos., then the base angles are congruent.
2. IE KE
2. If the triangle is isos., then the legs are congruent
4. KET
IEA
4. SAS (1,2,3)
A
K
M
S
E TR
S R
1. RK ET ;
MRMT ;
A is the mp. of MR;
S is the mp. of MT
1. Given
2. R T 2. If sides, then angles.
3.
RAAM ;TSSM
3. Mp. divides segments into 2 congruent segments.
RAK 5. TSE5. SAS ( 4, 2, 1)
4. RA TS4. Same as 3.
6. AK SE 6. CPCTC
Given: RK ET
MT MR
A is the mp of MR
S is the mp of MT
Prove: AK SE
Works Cited
Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry: For Enjoyment and Challenge. Evanston, Illinois: McDougal Littell, 1991. Print.