GEOMETRY 5.5 GEOMETRY 5.5 Review of 5.4 – Angles & Sides of a Triangle.

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The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

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Presentation transcript:

GEOMETRY 5.5 GEOMETRY 5.5 Review of 5.4 – Angles & Sides of a Triangle

GEOMETRY 5.5 Review of 5.4 – Angles & Sides of a Triangle

GEOMETRY 5.5 Review of 5.4 – Angles & Sides of a Triangle

GEOMETRY 5.5 Review of 5.4 – Angles & Sides of a Triangle

The PERPENDICULAR segment from a Point to a Line IS the SHORTEST Segment from the Point to the Line. Given: P Prove: 2 1 j Q A

GEOMETRY 5.5

GEOMETRY 5.5

GEOMETRY 5.5

GEOMETRY 5.5 GEOMETRY 5.5

GEOMETRY 5.5 GEOMETRY 5.5 To Determine whether 3 lengths could make a Triangle:

GEOMETRY 5.5 GEOMETRY 5.5 To Determine whether 3 lengths could make a Triangle: ADD the Two Smallest Lengths (a + b)

GEOMETRY 5.5 GEOMETRY 5.5 To Determine whether 3 lengths could make a Triangle: ADD the Two Smallest Lengths (a + b) Compare the SUM to the Longest Length (c)

GEOMETRY 5.5 GEOMETRY 5.5 To Determine whether 3 lengths could make a Triangle: ADD the Two Smallest Lengths (a + b) Compare the SUM to the Longest Length (c) To make a Triangle: a + b > c

GEOMETRY 5.5

GEOMETRY 5.5

GEOMETRY 5.5

GEOMETRY 5.5

x + a > b a + b > x To determine the RANGE of possible Lengths of the 3rd side of a Triangle: Given length a and b, with a < b Find the RANGE of the third side, x Lower Limit: Upper Limit: x + a > b a + b > x

GEOMETRY 5.5

GEOMETRY 5.5 REMEMBER: Distance between 2 points on the graphing plane:

GEOMETRY 5.5

GEOMETRY 5.5

GEOMETRY 5.5

GEOMETRY 5.5 AB + BC > AC BC + AC > AB AC + AB > BC

GEOMETRY 5.5 GEOMETRY 5.5 PQ + QR > PR QR + PR > PQ PR + PQ > QR

GEOMETRY 5.5 R O Given: Triangle ROS Prove: SO + OR > RS S

GEOMETRY 5.5 GEOMETRY 5.5 R O Given: Triangle ROS T Prove: SO + OR > RS S Start: Draw segment OT so that OT = SO

GEOMETRY 5.5 D Given: Prove: BD + DC > AC 1 2 A B C

GEOMETRY 5.5 Given: D Prove: BE + ED + AC > DC E 1 2 A B C

GEOMETRY 5.5

GEOMETRY 5.5