Warm Up What’s Wrong With Each Picture? 38° 65° 75°

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Presentation transcript:

Warm Up What’s Wrong With Each Picture? 38° 65° 75°

Homework pg. 1104-1108 (4-9, 12, 13, 19, 20)

Explore Triangle Inequalities Objective Explore Triangle Inequalities

I need a volunteer! Give me the lengths of the sides of a triangle with a perimeter of 16 units. https://www.geogebra.org/m/130

Another Way to Think about it…

Triangle Inequality Theorem pg. 1112

Tell whether a triangle can have sides with the given lengths. Explain. 7, 10, 19 No—by the Triangle Inequality Theorem, a triangle cannot have these side lengths.

Tell whether a triangle can have sides with the given lengths. Explain. 2.3, 3.1, 4.6    Yes—the sum of each pair of lengths is greater than the third length.

Your Turn. pg. 1113 (6, 7)

The lengths of two sides of a triangle are 8 inches and 13 inches The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third side. x + 8 > 13 8 + 13 > x x > 5 21 > x Combine the inequalities. So 5 < x < 21. The length of the third side is greater than 5 inches and less than 21 inches.

The lengths of two sides of a triangle are 22 inches and 17 inches The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the third side. x + 17 > 22 22 + 17 > x 39 > x x > 5 Combine the inequalities. So 5 < x < 39. The length of the third side is greater than 5 inches and less than 39 inches.

Your Turn! pg. 1115 (9, 10)

In Which Alligator’s Mouth Can I fit the largest stick? 2 1 3

Which side of the triangle is the longest? The largest angle is F, so the longest side is .

Which stick will have the largest alligator mouth? 1 2 3

Which angle of the triangle is the largest? The longest side is , so the largest angle is C.

Side and Angle Relationships in Triangles pg. 1115 pg. 1116

Write the angles in order from smallest to largest. The angles from smallest to largest are F, H and G.

Write the sides in order from shortest to longest. The sides from shortest to longest are

Your Turn! pg. 1116 (11, 12) pg. 1117 (13, 14)

Exit Ticket Write the angles in order from smallest to largest. 2. Write the sides in order from shortest to longest. 3. The lengths of two sides of a triangle are 17 cm and 12 cm. Find the range of possible lengths for the third side. 4. Tell whether a triangle can have sides with lengths 2.7, 3.5, and 9.8. Explain.

Homework Review Sheet