Download 5.6 Hinge Theorem

Geometry Chapter 5: Relationships within Triangles 5.6-­‐ Hinge Theorem and Indirect Proof SWBAT: use inequalities to make comparisons in two triangles. Common Core: G.CO.10
“Do Now” Can the 3 given side lengths make up a triangle? 1. 2, 6, 3 4. List the sides in order from shortest to longest. 2. 8, 11, 16 3. 5, 10, 5 5. List the angles in order from smallest to largest. You are given a 14-­‐inch piece of wire. You want to bend the wire to form a triangle so that each side length is a whole number. 6. Identify the possible side lengths of two 7. Identify the possible side lengths of a isosceles triangles. scalene triangle. 8. List two combinations of segment lengths that will not produce triangles. Geometry Chapter 5: Relationships within Triangles Theorem 5.13-­‐ Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Theorem 5.14-­‐ Converse of the Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second. 1. Which of the following is a possible length for !!!
𝐽𝐾 : 19cm, 21cm, or 24cm? 2. Which of the following is a possible measure for ∠𝑂: 20°, 22°, or 26°? Complete the statement with <, >, or = 3. UW _________ TX 4. 𝑚∠1 _________ 𝑚∠2 Geometry Chapter 5: Relationships within Triangles Use an inequality to describe the restriction on the value of x as determined by the Hinge Theorem or its converse. 8. In ∆𝐴𝐵𝐶 and ∆𝑋𝑌𝑍, 𝐴𝐵 = 𝑌𝑍, 𝐴𝐶 = 𝑌𝑋, 𝐵𝐶 = 9𝑖𝑛, 𝑋𝑍 = 11𝑖𝑛. , 𝑎𝑛𝑑 𝑚∠𝐴 = 47°. Which of the following is a possible measure for ∠𝑌: 35°, 42°, 47°, 𝑜𝑟 53°? Complete the following statement with <, >, or = Geometry Chapter 5: Relationships within Triangles Indirect Reasoning 15. Write an indirect proof that an odd number is not divisible by 4. Homework: Pgs. 348 – 349 #’s 1 – 17 ODD