Geo 9 h 6 H 6 INQULITIS SSIGNMNT SHT H 6 SUPPLMNTRY #, 6. 06-7 #,,6,8- SUPPLMNTRY # 6. Indirect proof 6-7 # 5,7,9,0,, SUPPLMNTRY #,5 6. for one triangle - #,,7-9 SUPPLMNTRY # 6 6.5 for two triangles - # - all Review TST HPTR SIX
Geo 9 h 6
Geo 9 h 6 Properties of ) dd > F If > and F, then what must be true? ) iv > If > and M and N are midpoints M Then N ) Transitive > If >, > F, then F ) xterior ngle Inequality: T > If < is equal to < + < then < 5) Parts
Geo 9 h 6. Using the figure to the right, fill in the blanks. R a) If x = 0 and y = 0, then w > y b) If y = 5 and z = 68, then w c) If w =, then x S w z Q x P d) If w = 50, then z e) If x = 5 and z = 90, then w f) If z = 90, then x and y ) Prove: < > <.. Given ) Prove:. O,. Given in interior of <O O
Geo 9 h 6 5 ) R S T Prove: ROT SOV. ROS TOV O V X ) Prove: < > <X R U. Figure as shown. Given T S
Geo 9 h 6 6 5). Given diagram X Prove: U T R S U 6) Prove: S V R. PS bisects <P. Given M P
Geo 9 h 6 7 INIRT PROOFS When proving things are not equal, it is easier to use an Indirect Proof F Given: F Prove: INIRT PROOF PROUR () ssume that the NGTION of the desired ONLUSION. () Write the chain of reasons until you reach an IMPOSSIILITY. () State ONTRITION and why. ( negates the given or a theorem or definition) () Write THRFOR ( ) the opposite of the assumption must be true.
Geo 9 h 6 8 P Given: R is not the midpoint of QS, PQ = PS Prove: PR does not bisect < QPS Q R S Given:, Prove:
Geo 9 h 6 9 Given : bisects is acute Prove: Given: =, P is a point on that is not the midpoint. Prove: P does not bisect P
Geo 9 h 6 0 h. 6. for one triangle Th 6-: If one side of a triangle is longer than a second side, then = 6, = 8, = 0 Which is largest angle? Th 6-: If one angle of a triangle is larger than a second triangle, then < = 50, < = 00, < = 0 Which is the largest side? orr : The perpendicular segment from a point to a line is orr : The perpendicular segment form a point to a plane is Th 6-: The sum of the lengths any two sides of a triangle is greater than MO: UT QUL STRIPS. TK ON N IVI INTO TWO UNQUL PRTS. TRY TO MK TRINGL. Possible triangles? a) 6,8,0 b),,8 c).5,., 5.0 d) 6, 5, x what does x have to be?
Geo 9 h 6 ) In triangle, =, = 7, = 9. Name the largest angle, the smallest angle. ) In triangle PQR, <P = 7, <Q = 7 and <R = 7. Name the largest side, the shortest side. ) For triangle MPS, name the angles in order of increasing length. M 0 M S 5 M P ) Given triangle GKH as marked. rrange the angles <GKH, <, <G, and <H in order of increasing size. K 5 G 9 M 5 H 5) Which segment is the longest? R P 65 6 60 M 5 7 K
Geo 9 h 6 6) Which segment is the shortest? S 70 5 5 R P 0 70 77 Q 7) Prove: < is the smallest angle of the triangle. > > 8) Prove: >. < > <, < > <
Geo 9 h 6 6.5 INQULITIS FOR TWO TRINGLS HING SS: If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. 8 8 9 9 HING SSS: If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is larger than the third side of the second, then the included angle of the first triangle is bigger than the included angle of the second triangle. Which is longer, or F? 5 8 F Which is bigger, < or <? F
Geo 9 h 6 () In WXYZ, XZ > WY. Prove : <XWZ > <WZY Fill in the letters. () Given: PQ = PR = RS Prove: QR < PS P Q R S
Geo 9 h 6 5 () Given: < < <,, > Prove: > () Given: < > < and < > < Prove: > (5) List the angles in order of size, starting with the largest. W 5 X 5 Z 9 Y Z
Geo 9 h 6 6 h 6 Geometry Review Worksheet () () 5 5 6 6 7 8 Given: =, m 5 > m Given: =, > Prove: m > m Prove: > () () 6 5 Given: > Prove: > Prove: + + > (5) (6) 5 6 Given: is a parallelogram Given: = m > m Prove: >
Geo 9 h 6 7 Prove: > (7) (8) (omit) 5 6 Given: m = m Given: = = = m > m Prove: m > m Prove: m 5 > m (9) (0) 6 5 Given: =, Given: Prove: Prove: > () Find the longest and shortest segments () If two sides of a triangle are 7 and 6, in the figure below. then the third side must be between and. 6 60 60 59
Geo 9 h 6 8 dditional Review ) 6 Given: = = 5 Prove: > ) Given: = Prove: > 7 8 9 5 6 5) Given: > = Prove: >
Geo 9 h 6 9 SUPPLMNTRY PROLMS. Graph triangle with = (-8,7) = (-, ) and = ( 5,7). List the sides of the triangle in increasing order. What do you think will happen to the order if I add to, to and to?. Which is the biggest angle, <, < or <.. What are the key steps to writing an indirect proof?. ut out two strips of paper the length of one side of a piece of paper. Take one of them and break it into pieces, not the same length. Try to make a triangle out of the pieces. 5. Go back to triangle from the first problem. Measure the angles. List the angles in increasing order. 6. Graph triangle with =(-0,8) = (-0,) = (0,). Find it s sides. Graph triangle SNO with S = (,0) N = (5,6) and O = (,6) Find its sides. Which angle is bigger, < or < NOS. Why do you think what you do?