Warm-up 1) Write an inequality to describe the length of MN. (Look at the picture) 2) Find the range for the measure of the third side of a triangle if two sides measure 4 and 13. 3) Can these 3 lengths for a triangle? a) 6, 6, 12b) 10, 8, 6c) 3, 2, 2

5-6 Inequalities in 2 Triangles

Hinge Theorem (You don’t have to write every word!) If 2 sides of a triangle are cong. to 2 sides of another triangle & the incl. ang. of 1 triangle is greater than the incl. ang. of the other triangle, then the 3 rd side of the 1st triangle is larger than the 3 rd side of the 2nd triangle. A B CX Y Z 5060

Converse Hinge Thm (you don’t have to write every word!) If 2 sides of a triangle are cong. to 2 sides of another triangle & the 3 rd side of 1 triangle is greater than the 3 rd side of the other triangle, then the ang. inside the cong. sides of the 1st triangle is larger than the ang. inside the cong. sides of the 2nd triangle. A B CX Y Z 15 20

Example Compare the measures AD and BD. Answer: By the Hinge Theorem, m  ACD > m  BCD, so AD > DB.

Example Compare the measures m  ABD and m  BDC. Answer: By the Converse of the Hinge Theorem, m  ABD > m  BDC.

TOO A.FG > GH B.FG < GH C.FG = GH D.not enough information Compare the lengths of FG and GH.

TOO A.m  JKM > m  KML B.m  JKM < m  KML C.m  JKM = m  KML D.not enough information Compare m  JKM and m  KML.

Think-Pair-Share! A.Meena’s kite B.Rita’s kite Meena and Rita are both flying kites in a field near their houses. Both are using strings that are 10 meters long. Meena’s kite string is at an angle of 75° with the ground. Rita’s kite string is at an angle of 65° with the ground. If they are both standing at the same elevation, which kite is higher in the air?

HW: WS 5-6 Practice