Triangles and Trapezoids

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Presentation transcript:

Triangles and Trapezoids Midsegments Triangles and Trapezoids

Midsegment What is it? Connects 2 midpoints of the sides (legs) How many does a triangle have? 3 How many does a trapezoid have? 1

Midsegment in a Triangle What is special about midsegments in Triangles? If all 3 are drawn you construct 3 congruent triangles Midsegments are parallel to the third side ( side not touch) and is half the length of the third side

Prove midsegment Properties Parallel and Half Prove Triangles are similar Proportional sides and congruent Angles. S R BD is midsegment of ACE G C = C Reflexive BC = 1/2 AC Def Midseg DC=1/2 AC ACE ~BCD SAS BD = 1/2 AF Def Similar <BDC=<AEC BD || AE Converse of Corr

Example

Trapezoid Midsegment Trapezoid is part of a triangle Midsegment is parallel to both bases What about the length? Average of the two bases

Example

Homework Review pg 272 7 and 8 Pg 277 1-8 Honors 10