Constructing Triangles

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Presentation transcript:

Constructing Triangles How many Triangles Can I make?

Triangle Inequality Theorem The third side of a triangle must be: Less than the sum of the other two sides. Greater than the difference of the other two sides. 4+6 = 10 9<10 6-4 = 2 9>2 9+6 = 15 4<15 9-6 = 3 4>3 9+4 = 13 6<13 9-4= 5 6>5 4 6 9

Example Can we create a triangle using sides of length 3,4, and 5? Can we construct a triangle using sides of length 4, 7, and 12? Yes! Why? No. Why?

90 + 110 = 200 200>180 Angles in a Triangle We learned that the angles in a triangle add to 180o. Ex. If I have an angle that is 900 and another angle that is 1100 can I create a triangle? Why? 90 + 110 = 200 200>180 So these angle measures cannot create a triangle!

Exterior and Remote Interior Angles An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side Adjacent means next to or adjoining For each exterior angle of a triangle, the two nonadjacent interior angles are called the remote interior angles

Triangle Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles m∠1 = m∠2 + m∠3 Ex: If m∠2 = 45 and m∠3 = 55, what is m∠1? m∠1 = 45 + 55 = 100

Examples Solve for x. Solve for y. 50o 60o x 40 y 112o

Exterior Angles m∠1 + m∠2 + m∠3 = 360o The exterior angles of a triangle add to 360o ∠ 2 ∠ 1 ∠ 3 m∠1 + m∠2 + m∠3 = 360o

Examples Can I construct a triangle with an exterior angle of 850 and remote interior angles that are 35o and 60o ? Can I construct a triangle with exterior angles 90o , 120o , and 80o ? If two exterior angles of a triangle are 110o and 115o what is the measure of the third exterior angle?

Constructing triangles Objective: To construct triangles using a protractor. 60º

Three ways to construct triangles. When constructing triangles we need a combination of angles and lengths. We can construct triangles with a compass if we have the lengths of the 3 sides (SSS). ( We won’t be looking at this one just yet) We can construct triangles using a protractor if we have the length of 1 side and the measurement of 2 angles (ASA ). We can construct triangles using a protractor if we have the length of 2 sides and the measurement of 1 angles ( SAS ). Note: To construct triangles, we need to know the length of at least 1 side plus 2 other pieces of information.

Given one side and two angles (ASA): Draw a triangle with one side 6cm and angles at each end of 30º and 70º. Mark 70º Mark 30º 6 cm

Given two sides and one angle ( SAS): Draw a triangle with a side 12 cm and side 9 cm with an angle of 75º between them. Mark 75º 12 cm

Practice Problems Construct the following triangles: A S A Triangles 40º 7cm 50º 45º 6 cm 45º 20º 8cm 100º 60º 8cm 60º 110º 7 cm 45º S A S Triangles 7cm 50º 4 cm 6 cm 45º 6 cm 8cm 100º 6 cm 8cm 60º 8 cm 7 cm 45º 6 cm