Relationships Between Sides and Angles in a Triangle

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Presentation transcript:

Relationships Between Sides and Angles in a Triangle How can you use the relationships between side lengths and angle measures in a triangle to solve problems?

Triangle: Angle and Side Relationships In a triangle, the largest angle is OPPOSITE the longest side. The smallest angle is OPPOSITE the shortest side. The midsize angle is OPPOSITE the midsize side.

Lets See What This Looks Like B 100 Triangle ABC has side lengths of : 7cm, 9cm and 4.5cm. Use the relationship between the sides and angles to match each side with its correct length. AC= 9cm The longest side is opposite the largest angle. AB= 4.5cm The shortest side is opposite the smallest angle. BC= 7cm The midsize side is opposite the midsize angle. 50 30 A C

Solving Problems Using Triangle Relationships Congruent means equal. **Recall that triangles can be classified by the lengths of their sides. A SCALENE triangle has NO congruent sides or angles. An ISOSCELES triangle has TWO congruent sides and angles. An equilateral triangle has THREE congruent sides and angles. Lets see how we can use this to solve a word problem!

Problem Solving Brandy is making a quilt where each block is made of four triangles. Each triangle is the shape of a right isosceles triangle. Two of the side measures of one triangle are 6.4 inches and 9 inches. Brandy wants to add a ribbon border. How much ribbon will she need?

Step by Step Step 1. Analyze and Identify Important information. I need to find the amount of ribbon Brandy needs for a border around one triangle. I know each quilt piece has the shape of a right isosceles triangle. I know two sides measure 6.4 inches and 9 inches.

Step by Step Step 2 Formulate a Plan I can draw a model and label it with the important information I already know, to find the total length of ribbon

Step by Step Step 3 Solve the problem Think: A right triangle will have one 90 degree angle. Since the sum of all angles is 180, the other two angle will be congruent (same) and will have a combined measure of 90. SO…90/2=45. EACH other angle is 45. Label the new info on your model. 90 is the GREATEST angle measure, so the side opposite will have the LONGEST length (9). The other two angles are congruent (same), so the side lengths will be congruent (same). They will both be 6.4 Label the new information on your model. Now that I know ALL the side lengths I can add to get the total ribbon needed!

YOU TRY! A fence around a rock garden is in the shape of a right triangle. Two of the angles measure 30 and 60. Two sides measure 10 feet and 17.3 feet. The TOTAL length of the fence is 47.3 feet. How long is the side OPPOSITE the right angle? **Start at step 1!