Geometry Ch. 5 Test Review

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Presentation transcript:

Geometry Ch. 5 Test Review

5-1 Midsegment Solve for x

5-2 Perpendicular Bisector / Angle Bisector Solve for x

5-3 Incenter Solve for x. Radii of circle X= -1 congruent

5-3 Graph the points. Find Circumcenter. Find Orthocenter. Perp bisectors 5-3 Graph the points. Find Circumcenter. Find Orthocenter. (0,0) altitudes (4,-3)

5-3 & 5-4 Point of Concurrency Name it! Perpendiculuar Bisector Median Altitude

5-3 Draw an angle bisector!

5-3-5-4 Point of Concurrency Name it! incenter Angle Bisectors Form _________________ Perpendicular Bisectors Form _____________ Medians Form __________________ Altitudes Form _________________ circumcenter centroid orthocenter

5-3-5-4 Point of Concurrency Name the line!

5-4 Centroid 10 5 12 36

5-6 List the SIDES in order. Smallest to largest. 54

5-6 Determine the SHORTEST side? Not EG 5-6 Determine the SHORTEST side? Look for next small L 47 X M S L M 67 DG O S

5-6 Write sides in order from smallest to largest DG, ED, EG/ EG, FG, EF L 47 X M S L M 67 O S

5-6 Longest side of triangle? In triangle ABC, m<A = 2x + 20, m<B = 4x – 30, m<C = x + 50. Solve for x. Find LONGEST side of triangle ABC. 2x + 20 + 4x – 30 + x + 50 = 180 7x + 40 = 180 7x = 140 x = 20

Continuation… Longest side.. In triangle ABC, m<A = 2x + 20, m<B = 4x – 30, m<C = x + 50. Solve for x. Find LONGEST side of triangle ABC. C m<A = 2(20)+20 = 60 70 A 60 50 m<B = 4(20) – 30 = 50 B m<C = 20 + 50 = 70 AB

5-6 Which lengths could be SIDES of a triangle? No, 2.5+5.5>8.5 2.5, 8.5, 5.5 6, 5, 11 5x, 8x, 12x No, 6+5>11 Yes, 5x+8x>12x

5-6 Triangle Inequality Find range of values. Small side + small side > 3rd side 5-6 Triangle Inequality Find range of values. If lengths of sides of a triangle are 2k+3 and 6k, then the third side must be greater than ________ and less than _________ 4k-3 8k+3 Small side + small side > 3rd side 2k+3 + 6k > x 2k+3 + x > 6k OR -2k -3 -2k -3 8k+3 > x x > 4k-3 x < 8k+3 Greater than Less than

AEB > BDC Big so Big By Hinge Theorem 5-7 Hinge Theorem & Converse of Hinge Theorem Fill in with <, >, or =. By which theorem? AEB > BDC so Big Big By Hinge Theorem

By Converse of Hinge Theorem 5-7 Hinge Theorem & Converse of Hinge Theorem Fill in with <, >, or =. By which theorem? AB<ED so Big By Converse of Hinge Theorem Big