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Transcript
Bell Work • Find the measure of the missing variables and state what type of angle relationship they have(alt. interior, alt. ext, same side interior, corresponding). • 1) 2) • 3) 4) Outcomes • I will be able to: • 1) Classify a triangle by its sides and/or angles • 2) Find the measure of interior angles of a triangle using the Triangle Sum Theorem • 3) Find the exterior angles of a triangle using the Exterior Angle Theorem Tablet Activity • Download the Geometry Pad app from the Playstore. • Do not download anything other than Geometry Pad, as this will slow down the download!!! • Set your tablet aside, we will use it later!!! Triangles • What is a triangle? • Triangle – A polygon formed by three segments joining three noncollinear points • Example: • There are two ways to classify triangle: • 1) By its sides • 2) By its angles Names Of Triangles Classifications By Sides • 1. Equilateral Triangles • Example: • What does it mean for a triangle to be equilateral? • ***All sides must be congruent Names of Triangles Classifications by Sides • 2. Isosceles Triangle • Example: • What does it mean for a triangle to be isosceles? • ***At least two sides are congruent • ***So, an equilateral triangle is also isosceles Names of Triangles Classification by Sides • 3. Scalene Triangle • Example: • What does it mean for a triangle to be scalene? • ***No sides are congruent Classify the following Triangles • 1) • 4) • 2) • 5) • 3) • 6) Names of Triangles Classification by Angles • 4. Acute Triangle • Example: • What do you notice about all of the angles? • ***An acute triangle has all acute angles Names of Triangle Classifications by Angles • 5. Equiangular Triangle • Example: • What do you notice about all of the angles? • They are all congruent • ***An equiangular triangle has all angles congruent • ***An equiangular triangle is also acute. Names of Triangles Classification by Angles • 6. Right Triangle • Example: • What do you notice about the angles? • There is one right angle • ***There is one right angle in every right triangle Names of Triangles Classification by Angles • 7. Obtuse Triangles • Example: • What do you notice about the angles? • ***There is one obtuse angle in every obtuse triangle Classifying Triangles • When classifying triangles, we can classify them by both their sides and their angles What type of triangle would this be? Right Isosceles Triangle or Isosceles Right Triangle We can name a triangle by angles or sides first Classifying Triangles Examples • How would you classify this triangle? • Obtuse Scalene Triangle Classifying Triangle Examples • How would you classify this triangle? • Acute Scalene Triangle Parts of Triangles • Vertex – Each point joining the sides of a A triangle • Example: • A, B, and C are all B C vertices • Adjacent Sides – The two sides sharing a vertex • AC and AB, AB and BC, AC and BC are adjacent sides Parts of Triangles A The sides that form the right angle hypotenuse AB and BC are the legs of this triangle leg The side opposite the right angle leg B C Tablet Activity • Plot the points from each problem and classify the triangles by looking at the measurements of their sides and angles • See the overhead on how to use the app and the answers for #1!!! Parts of Triangles leg The non-congruent side of an isosceles triangle The congruent sides of an isosceles triangle base leg Types of Angles in Triangles • There are both interior and exterior angles we are concerned with when looking at triangles • Interior angle are inside the triangle • Exterior angles are outside the triangle Triangle Sum Think about the angle sums!!! 67 50 43 90 70 • We can conclude that all the angles add to 180° 40 Triangle Sum Theorem Exterior Angle Theorem 60 80 90 40 =120 Compare the inside angles to the outside angle 30 • We can conclude that the sum of the remote interior angle is equal to the exterior angle A B 1 Exterior Angle Theorem Examples • • • • • How can we solve this? 42 + 90 + x = 180 132 + x = 180 -132 -132 x = 48 Examples • • • • • • • How can we solve this? x+ 110 = 4x – 7 -x -x 110 = 3x – 7 +7 +7 117 = 3x 39 = x Examples • How can we solve this? • Remember, we can label things we know even if they are not in our picture. • Now we have, • 33 + x + 90 = 180 • 123 + x = 180 • -123 -123 • x = 57 90 Examples • How can we solve this? • • • • • x + x + 30 = 180 2x + 30 = 180 - 30 - 30 2x = 150 x = 75 Independent Practice • 1) Solve for the missing variable • 2) Circle the chart • r + 53 + 37 = 180 • r + 90 = 180 • r = 90