1. Daily Warm Up Quiz 1. Define: isosceles triangle 2. Complete each theorem below: If a triangle is isosceles, then __________. If the base angles of a triangle are congruent, then ______________________. 3.Find the missing measure: x

2. Relationships Within Triangles Midsegments in Triangles

3. Midsegments of Triangles At the end of this lesson, you should be able to use properties of midsegments to solve problems.

4. Definition: Midsegment of a Triangle A midsegment of a triangle _____ ___________________________ ___________________________ ___________________________ is a segment in a triangle which connects the midpoints of opposite sides. 5 5 6 6 A B Note: A is a midpoint. B is a midpoint. AB is a midsegment.

5. Midsegment of a Triangle How many midsegments are there in any triangle? 3 3 4 4 5 5 3 Three midsegments can be constructed in any triangle.

6. Triangle Midsegment Theorem If a segment in a ∆ is a midsegment, then it  is // to the third side  has length ½ the third side.

7. Identifying Midsegments in Triangles 3 3 3 4 4 7 5 A A A A BC B B B C C C 6 6 55 5 4 45 46 6 97 7 7 8 7 7 88 Identify A, B, or C as a midsegment, then determine its length. B = 6 C = 7.5 A = 8 C = 4.5 You can use Triangle Midsegment Theorem to determine missing measures in triangles.

8. Using Triangle Midsegment Theorem to Find Missing Measures Q and P are the midpoints of ∆ RST. What is m RS?...m TQ?....m TS? R x + 50 P x + 85 Q S T 3x + 46 A B C 110 70 F E D 1. Find the measure of the following: a.) ∠ ABC b.) ∠ D c.) ∠ A d.) ∠ CBF 70 40 110 x Check Here!

9. Final Checks: Architecture The triangular face of the Rock ‘n’ Roll Hall of Fame in Cleveland is isosceles. The length of the base is 229 ft. 6 in. What is the length of the highlighted segment?

10. Final Checks for Understanding 1.Define midsegment of a triangle. 2.Name two properties of midsegments in triangles. 3.Find the missing measures, given a is a midsegment. a 24 x 64 26 y x = _____; y = _____ Homework:

11. Check Your Solution Here: Click here to return to today’s lesson: PQ = ½ ST x + 85 = ½ (3x + 46) 2(x + 85) = 3x + 46 2x + 170 = 3x + 46 2x = 3x – 124 -x = -124 x = 124 PS = x TS = 3x + 46 PS = 124 TS = 3 (124) + 46 RS = RP + PS TS = 372 + 46 RS = 124 + 124 TS = 418 RS= 248 TQ = QR TQ = x + 50 TQ = 124 + 50 TQ = 174