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Daily Warm Up Quiz

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 ______________________. Find the missing measure:. x. Relationships Within Triangles

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Daily Warm Up Quiz

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  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 ______________________. • 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 is a segment in a triangle which connects the midpoints of opposite sides. A midsegment of a triangle ______________________________________________________________________________________ Note: A is a midpoint. B is a midpoint. AB is a midsegment. 5 6 B A 6 5

  5. Midsegment of a Triangle How many midsegments are there in any triangle? 3 4 3 4 3 5 5 5 5 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 Identify A, B, or C as a midsegment, then determine its length. B = 6 3 C = 4.5 5 5 4 3 A 5 A 7 5 5 3 B C B C 4 4 6 6 C = 7.5 A = 8 6 4 7 7 7 A A 4 7 8 6 B C B C 8 8 7 9 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 ST 3x + 46 A B C 110 70 F E D Check Here! 1. Find the measure of the following: a.) ∠ ABC b.) ∠ D c.) ∠ A d.) ∠ CBF 70 70 x 40 110

  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 • Define midsegment of a triangle. • Name two properties of midsegments in triangles. • Find the missing measures, given a is a midsegment. a x x = _____; y = _____ 24 Homework: 64 26 y

  11. Check Your Solution Here: 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 PQ = ½ ST x + 85 = ½ (3x + 46) 2(x + 85) = 3x + 46 2x + 170 = 3x + 46 2x = 3x – 124 -x = -124 x = 124 Click here to return to today’s lesson:

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