Splash Screen

Concept

Concept

By the Exterior Angle Theorem, you know that mÐ1 = mÐ2 + mÐ3. The definition of inequality and the properties of inequalities can be applied to the measures of angles and segments, since these are real numbers. Consider Ð1, Ð2, and Ð3 in the figure shown. By the Exterior Angle Theorem, you know that mÐ1 = mÐ2 + mÐ3. Since the angle measures are positive numbers, we can also say that mÐ1 > mÐ2 and mÐ1 > mÐ3 by the definition of inequality. Concept

Concept

Use the Exterior Angle Inequality Theorem Example 1

Use the Exterior Angle Inequality Theorem Example 1

The longest side and largest angle of ∆ABC are opposite each other The longest side and largest angle of ∆ABC are opposite each other. Likewise, the shortest side and smallest angle are opposite each other. Concept

Concept

List the angles of ΔABC in order from smallest to largest. Order Triangle Angle Measures List the angles of ΔABC in order from smallest to largest. Example 2

List the sides of ΔABC in order from shortest to longest. Order Triangle Side Lengths List the sides of ΔABC in order from shortest to longest. Example 3

Angle-Side Relationships HAIR ACCESSORIES Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie? Example 4

End of the Lesson

Five-Minute Check (over Lesson 5–2) CCSS Then/Now Key Concept: Definition of Inequality Key Concept: Properties of Inequality for Real Numbers Theorem 5.8: Exterior Angle Inequality Example 1: Use the Exterior Angle Inequality Theorem Theorems: Angle-Side Relationships in Triangles Example 2: Order Triangle Angle Measures Example 3: Order Triangle Side Lengths Example 4: Real-World Example: Angle-Side Relationships Lesson Menu

Find the coordinates of the centroid of the triangle with vertices D(–2, 9), E(3, 6), and F(–7, 0). B. (–3, 4) C. (–2, 5) D. (–1, 4) 5-Minute Check 1

Find the coordinates of the orthocenter of the triangle with vertices F(–1, 5), G(4, 4), and H(1, 1). A. B. C. (2, 3) D. 5-Minute Check 2

In ΔRST, RU is an altitude and SV is a median In ΔRST, RU is an altitude and SV is a median. Find y if mRUS = 7y + 27. ___ A. 5 B. 7 C. 9 D. 11 5-Minute Check 3

In ΔRST, RU is an altitude and SV is a median. ___ Find RV if RV = 6a + 3 and RT = 10a + 14. A. 3 B. 4 C. 21 D. 27 5-Minute Check 4

Which of the following points is the center of gravity of a triangle? A. centroid B. circumcenter C. incenter D. orthocenter 5-Minute Check 5

G.CO.10 Prove theorems about triangles. Mathematical Practices Content Standards G.CO.10 Prove theorems about triangles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS

You found the relationship between the angle measures of a triangle. Recognize and apply properties of inequalities to the measures of the angles of a triangle. Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle. Then/Now