4/20 Triangle Midsegment.

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4/20 Triangle Midsegment.

Presentation transcript:

4/20 Triangle Midsegment

Do Now If m∠1=3x and m∠4=3x–6 in the diagram below, find m∠2 if ∠3 is a right angle. Hint: <1 + <3 + <4 = 180 Essential Question: How can we determine the midsegment of a triangle?

Agenda Do Now Good Things Review Triangle Sum Theorem Exterior Angle Theorem Properties of Isosceles Triangles Notes: Midsegment of a Triangle Exit Ticket

Good Things!

Review: Triangle Congruence Postulates The order that we name triangles in is very important! ∆ABC is congruent to ∆XYZ What do we know to be true? 5 congruence postulates (rules that help us prove triangles are congruent SSS, SAS, ASA, AAS, HL

Review: Transversals List all of the congruent angles Alternate interior Alternate exterior Corresponding Vertical List all of the supplementary angles Same side interior Same side exterior

Review: Transversals Find m<5 if m<3 = 6x + 18 and m<5 = 12x.

Review: Triangle Sum Theorem Find m<B.

Notes: Isosceles Triangles The base angles of an isosceles triangle are congruent The legs of an isosceles triangle are congruent

Review: Isosceles Triangles Find m<A.

Notes: Triangle Midsegment Theorem The midpoint is the point on a line segment that divides it into two equal parts. Midsegment of a triangle - a line segment that joins the midpoints of two sides of a triangle Midpoint Midsegment The midpoint of AB is D The midpoint of AC is E The midsegment is line DE

Notes: Triangle Midsegment Theorem A midsegment of a triangle is parallel to the base and is half as long as the base. ___ ___ AC || XY ___ ___ XY = ½ * AC

Triangle Midsegment Theorem Find the lengths of side BC and side YZ What do we know? How can we solve for BC? How can we solve for YZ? Solve for BC by using the midsegment XZ and multiplying it by 2 Solve for YZ by dividing AB by 2 AXZ  think of it like a transversal. If ZY is parallel to AB, then Angle AXZ is an alternate interior angle to XZY, so they are congruent  38 degrees

Triangle Midsegment Theorem If AB = 2x + 7 and YZ = 3x – 6.5, what is the length of AB?

Your Turn!

Partner Practice Worksheet This worksheet is your exit ticket We will do a self-check at the end of class My goal is for this to help you on the independent practice that is due tomorrow! You will be graded on the work you do in class, NOT on how many you get correct