Angle-Side Relationship  You can list the angles and sides of a triangle from smallest to largest (or vice versa) › The smallest side is opposite.

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Presentation transcript:

Angle-Side Relationship

 You can list the angles and sides of a triangle from smallest to largest (or vice versa) › The smallest side is opposite the smallest angle › The longest side is opposite the largest angle Angle-Side Relationship

List the angles of Δ ABC in order from smallest to largest. Answer:  C,  A,  B Angle-Side Relationship

A. A B. B C. C D. D List the sides of Δ RST in order from shortest to longest. A. RS, RT, ST B. RT, RS, ST C. ST, RS, RT D. RS, ST, RT Angle-Side Relationship

Compare the measures AD and BD. Answer: m  ACD > m  BCD, so AD > DB. In ΔACD and ΔBCD, AC  BC, CD  CD, and  ACD >  BCD. Inequalities in Triangles

Compare the measures  ABD and  BDC. Answer:  ABD >  BDC. In ΔABD and ΔBCD, AB  CD, BD  BD, and AD > BC. Inequalities in Triangles

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

Note that there is only one situation that you can have a triangle; when the sum of two sides of the triangle are greater than the third.  They have to be able to reach!!

 AB + BC > AC A B C  AB + AC > BC  AC + BC > AB

Example: Determine if the following lengths are legs of triangles A)4, 9, ? 9 9 > 9 We choose the smallest two of the three sides and add them together. Comparing the sum to the third side: B) 9, 5, 5 Since the sum is not greater than the third side, this is not a triangle ? 9 10 > 9 Since the sum is greater than the third side, this is a triangle

Example: a triangle has side lengths of 6 and 12; what are the possible lengths of the third side? 6 12 X = ? = – 6 = 6 Therefore: 6 < X < 18

The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D B C E A D and E are midpoints DE is the midsegment

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. DE ║AC D B C E A

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

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

In the diagram, ED and DF are midsegments of triangle ABC. Find DF and AB. DF = ________AB = ________ X  4 5X+2 x = ________ 10