Warm-Up #26

homework Lesson 2: Triangle Side Splitter Front side

Side-Splitter Theorem

Side-Splitter Theorem Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. OR

Side-Splitter Proof Statements Reasons 1. 2. 3. 4. 5. 6. 7.

Proof: http://mathbitsnotebook.com/Geometry/Similarity/SMSplitter.html

Side-Splitter Theorem Find the value of x. Find the value of x.

Corollary to Side-Splitter Theorem Corollary to Theorem 7-4: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

Application Given that the edges of the panels of the sails are parallel, find the values of the variables.

You wanna try one? Too bad! ;) Find the values of the variables in the following figure.

Homework Relationship of Triangles

Relationship of Similar Triangles

Triangle-Angle-Bisector Theorem Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Triangle-Angle-Bisector Theorem Find the value of x in the following figure. Find the value of x in the following figure.

Kick it up a notch!!! Find the value of x.

Kick it up a notch!!! Find the value of x.

Midsegments of Triangles Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half of its length Midsegment = ½ of Base Midsegment x 2x

Find the length of the midsegment. M = ½ b 23 M = ½ • 46 46 M = 23

Find the length of the base. M = ½ b 46 2• 46= ½ b 2• 92 92 = b

Find the length of the midsegment and the base. 5•3-1 = 14 M = ½ b 5x - 1 5x - 1 = ½(6x + 10) 5x - 1 = 3x + 5 6x + 10 -3x -3x 2x - 1 = 5 6•3+10 = 28 +1 +1 2x = 6 2 2 x = 3

Midsegments of Triangles In ΔEFG, H, J, and K are midpoints. Find HJ, JK, and FG. F HJ: JK: FG: 60 H J 40 G E K 100

Midsegments of Triangles AB = 10 and CD = 18. Find EB, BC, and AC A B E D C EB: BC: AC:

Midsegments Find m<VUZ. Justify your answer. 65° X Y V Z U

In the diagram, ST and TU are midsegments of triangle PQR In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU. 5 ft 16 ft TU = ________ PR = ________

In the diagram, XZ and ZY are midsegments of triangle LMN In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY. 14 cm 53 cm ZY = ________ MN = ________