Flashcards
Chapter 5 Geometry
Cards in this deck (14)
- 1exterior anglethe angle formed when a side of a triangle is extended past the outside
- 2remote angle(s)the angle(s) in a triangle not adjacent to the ext. angle
- 3chorda segment with endpoints on a circle
- 4diametera chord that goes through the center of the circle
- 5TSAI proof a. angle BCD=BDC why? b. angle BDC > BAC why? c. angle BCD > angle BAC d. angle BCA = angle BCD + angle DCA why? e. angle BCA > angle BCD why? f. angle BCA > angle BAC why?CONSTRUCT D WHICH MAKES BC=BD
a. ITT
b. TEAI
c. substitution
d. angle addition
e. def. of greater than
f. BCA > BCD BCD > BAC
transitive - 6TASI proof Given: C > A Prove: AB > BC Assumption: ?assumption: AB is less than or equal to BC
- AB = BC
A = C by ITT
C > A by given (contradiction)
BC > AB
A > C by TSAI
C > A by given (contradiction)
assumption is wrong, AB > BC - 7Hinge proof Given: AB=BC Prove: angles one and two are obtuse1. AB = BC 1.given
2. <3 = <4 2. ITT
3. <3 and <4 are acute 3. only one obtuse/right angle
4. <1 and <2 are obtuse 4. form LP with 3 & 4 - 8Converse Hinge Proof Given: AC = RT, AB = RS, ST > BC Prove: R > A assumption: ?assumption: A > R or R = A
-A > R
BC > ST by Hinge
ST > BC by given (contradiction)
- R = A
Tri. ABC = tri. RST by SAS
BC = ST by CPCTC
ST > BC by given (contradiction)
assumption is wrong, R > A - 9Hypotenuse Proof Given: B is right Prove: ?Prove: AC > AB
1. B is right 1. given
2. A and C are acute 2.only one rt
3. B > A ; B > C 3. rt>acute
4. AC > AB 4.TASI - 10Distance from Point to Line Proof Given: ? Prove: ?Given: line m, Q and R on m. P not on m, PQ perp. to m
Prove: PQ < PR
1. PQ perp. m 1. given
2. Q is right 2. def. of perp.
3. R is acute 3. TAST corollary
4. Q > R 4. right > acute
5. PR > PQ 5. TASI - 11Equal Perpendiculars Distance Proof Given: ? Prove: ?ADD BC
Given: AC & BD perp. to m and n
Prove: AC = BD
1. ...... 1. given
2. BC = BC 2. reflexive
3. A & D are right 3. def of perp.
4. ABC = BCD 4. AIAC
5. tri. ABC = tri. BCD 5.AAS
6. AC = BD 6. CPCTC - 12Triangle Inequality Proof a. CAD = CDA why? b. BAD = BAC + CAD why? c. BAD > CAD why? d. BAD > CDA why? e. BD > AB why? f. BD = BC + CD why? g. BD = BC + AC why? h. BC + AC > AB why?a. ITT
b. angle addition
c. def. of greater than
d. substitution
e. TASI
f. segment addition
g. substitution
h. substitution - 13Diameter is longest chord proof Prove: CD > AB1. AM + MB > AB 1. tri. ineq.
2. CM = MA = MB = MD 2.radii
3. CM + MD > AB 3. substitution
4. CM + MD = CD 4. segment add.
5. CD > AB 5. substitution - 14distancethe length of the shortest segment connecting two figures
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- Flashcards on Chapter 5 Geometry, created by ghill21 on 14/11/2014.
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