WarmUp Exercises WarmUp In Exercises 1 and 2
- Slides: 12
Warm-Up Exercises Warm-Up In Exercises 1 and 2, list the sides or angles in order from least to greatest. 2. 1. ANSWER R, ANSWER AB, BC, AC Tell whether the side lengths can form a triangle. 3. 37 m, 35 m, 18 m 4. 3 ft, 6 ft ANSWER yes ANSWER no T, S
5. 6 Inequalities Involving Two Triangles • SAS Inequality/Hinge Theorem – If 2 sides of one ∆ are congruent to 2 sides of another ∆ and the included ے in one ∆ has a greater measure than the included ے in the other, then the 3 rd side of the 1 st ∆ is longer than the 3 rd side of the 2 nd ∆.
Example • Since ے H > ے M, then JI > LK
Converse of the Hinge Theorem/SSS Inequality Theorem ● If 2 sides of one ∆ are congruent to 2 sides of another ∆ and the 3 rd side in one ∆ is longer than the 3 rd side in the other, then the ے between the pair of congruent sides in the 1 st ∆ is greater than the corresponding ے in the 2 nd ∆. Since JI > LK: ● ے H > ے M
Warm-Up 1 Exercises EXAMPLE Use the Converse of the Hinge Theorem Given that ST PR , how does PST compare to SPR? SOLUTION You are given that ST PR and you know that PS PS by the Reflexive Property. Because 24 inches > 23 inches, PT >RS. So, two sides of STP are congruent to two sides of PRS and the third side in STP is longer. ANSWER By the Converse of the Hinge Theorem, m PST > m SPR.
Warm-Up 2 Exercises EXAMPLE Solve a multi-step problem BIKING Two groups of bikers leave the same camp heading in opposite directions. Each group goes 2 miles, then changes direction and goes 1. 2 miles. Group A starts due o east and then turns 45 toward north as shown. Group B starts o due west and then turns 30 toward south. Which group is farther from camp? Explain your reasoning.
Warm-Up 2 Exercises EXAMPLE Solve a multi-step problem SOLUTION Draw a diagram and mark the given measures. The distances biked and the distances back to camp form two triangles, with congruent 2 mile sides and congruent 1. 2 mile sides. Add the third sides of the triangles to your diagram. Next use linear pairs to find and mark the included angles of 150° and 135°. ANSWER o o Because 150 > 135 , Group B is farther from camp by the Hinge Theorem.
Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Use the diagram at the right. 1. If PR = PS and m QPR > m is longer, SQ or RQ ? ANSWER RQ QPS, which
Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Use the diagram at the right. 2. If PR = PS and RQ < SQ, which is larger, RPQ or SPQ? ANSWER SPQ
Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 3. WHAT IF? In Example 2, suppose Group C leaves camp and goes 2 miles due north. Then they turn 40° toward east and continue 1. 2 miles. Compare the distances from camp for all three groups. ANSWER Group B is the farthest from camp, followed by Group C, and then Group A which is the closest.
Practice: Complete each statement
Warm-Up Exercises Complete each statement with < , > , or =. 1. KL ? NP ANSWER 2. m < 1 ? m ANSWER < 2
