5-1: Midsegments of a Triangle

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Presentation transcript:

5-1: Midsegments of a Triangle

What are the 3 pairs of parallel segments in the triangle?

What are the parallel segments? In ΔXYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.

In ΔQRS, T, U, and B are midpoints In ΔQRS, T, U, and B are midpoints. What are the lengths of TU, UB, and QR?

Using the Midsegment Theorem

5-2: Perpendicular and Angle Bisectors

What is the length of AB?

What is the length of QR?

What is the length of RM?

What is the length of FB?

5-3: Bisectors in Triangles

What are the coordinates of the circumcenter with vertices P(0, 6), Q(0, 0), and R(4, 0)?

GE = 2x – 7 and GF = x + 4. What is GD?

QN = 5x + 36 and QM = 2x + 51. What is QO?

5-4: Medians and Altitudes

If XA = 8, What is the length of XB? If ZC = 9, What are ZA and AC?

For ΔPQS, is PR a median, an altitude, or neither?

For ΔABC, is AD a median, an altitude, or neither?

5-6: Inequalities in One Triangle

Why is the measure of angle 2 greater than the measure of angle 3?

List the sides of ΔTUV in order from least to greatest

Can a triangle have sides with the given lengths? 3 ft, 7 ft, 8 ft 5 in, 10 in, 15,int 2 yds, 6yds, 9yds

Two side of a sandbox are 5ft and 8ft long Two side of a sandbox are 5ft and 8ft long. What is the possible range for the third side?

5-7: Inequalities in Two Triangles

What inequality relates LN to OQ in the figure?

What is the range of possible values for x?

Statements Reasons 1) 2) 3) 4) 5) 1) 2) 3) 4) 5)