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Investigating Angles in Triangles Free Geometry lesson from Bethany @ MathGeekMama.com Thank you for downloading this resource from MathGeekMama.com! I love providing high quality math teaching resources for parents and educators, but I ask that you please abide by the following terms of use. This allows me to continue providing resources for free! Thank you for your honesty and support of my work! Please do: • Download to your computer for personal use in the home or classroom • Print copies for your personal use Please do NOT: • Link directly to the pdf file • Save or store the file on your website • Edit this resource in any way • Print this resource to sell or distribute to others. If you would like to share this (or other) resources with friends or colleagues, please direct them to my website to download a copy for themselves. Thank you! Teaching Tips for Exploring the Angles in Triangles: Materials Needed: • Student handouts • Construction paper • Scissors Interior angles: The goal of this investigation is to discover that the sum of the angles inside a triangle is 180 degrees. This requires that students know that a straight line is equal to 180 degrees. If you ask before starting and there is some debate or uncertainty, allow students to draw a line and measure with a protractor. Or simply look at the protractor more closely. After cutting out triangles for their investigation, be sure students mark the angles. This will be very important because once they cut off the angles to measure them, 3 new triangles will be formed and you don’t want them to have to guess which angle was actually a part of their original triangle. Exterior angles: The second investigation looks at adjacent exterior angles. You may point out (or students may observe) that by extending one of the sides, a straight line is formed, and therefore the sum of the adjacent interior angle and the new exterior angle will equal 180 degrees. This is important to remember, and may help students with the investigation. The goal of this is to see that the exterior angle is equal to the sum of the two interior angles opposite (not touching) the exterior angle formed. I tried to draw a diagram to make it clear which angles are to be compared (and which angles need to be cut off), but students may need clarification on this. You may want to cut apart a triangle together as a class before letting students try with their own triangles. In addition, answers to the discussion questions are included at the end of this lesson. Have Fun Exploring Triangles! © 2016 MathGeekMama.com Interior Angles of Triangles Directions: Use a piece of construction paper to cut out 4 different triangles. They can be any size. Then use your triangles to complete the investigation below. Step 1: Draw an gle markin gs in each corner of each triangle so that you know where the interior angles are. Then cut the corners (angles) off of triangle 1. Lay the angles side by side along the line below and measure the total (in degrees) using your protractor. Record the answer below. Then repeat the process for your other 3 triangles. Triangle 1 interior angles are equal to: Triangle 2 interior angles are equal to: _____________ degrees _____________ degrees Triangle 3 interior angles are equal to: Triangle 4 interior angles are equal to: _____________ degrees _____________ degrees Step 2: For any triangle, the sum of the interior angles is equal to: ________________________ © 2016 MathGeekMama.com Exterior Angles of Triangles Directions: Use a piece of construction paper to cut out 2 different triangles. They can be any size. Then use your triangles to complete the investigation below. Step 1: The purpose of this investigation is to determine the angle outside of your t rian gle (either side will work). For example, in the diagram below, we are trying to determine the measure of angle d. Place your first triangle on the line below, similar to the diagram. Label your angles and then cut off the interior angles opposite the e xterior an gle you are trying to measure. (For example, in the diagram below, we would cut off angles a and b). Line up the 2 angles you cut off with the third interior angle to try and determine the measure of the exterior angle. Do the same with your second triangle. a b c d © 2016 MathGeekMama.com Exterior Angles of Triangles Step 2: Think About It… 1. How do the two interior angles compare to the exterior angle? _______________________________________________________________________________________________________________________________________ 2. Do you think this is true for any triangle? Why? _______________________________________________________________________________________________________________________________________ 3. Can you write a mathematical formula for the measure of the exterior angle? _______________________________________________________________________________________________________________________________________ Step 3: Solve it. Find the measure of the angles indicated below. b 60o c 15o a 90o a = ______________ 135o 115o b = ______________ © 2016 MathGeekMama.com 80o c = ______________ Interior Angles of Triangles Directions: Use a piece of construction paper to cut out 4 different triangles. They can be any size. Then use your triangles to complete the investigation below. Step 1: Answer Key Draw an gle markin gs in each corner of each triangle so that you know where the interior angles are. Then cut the corners (angles) off of triangle 1. Lay the angles side by side along the line below and measure the total (in degrees) using your protractor. Record the answer below. Then repeat the process for your other 3 triangles. Triangle 1 interior angles are equal to: Triangle 2 interior angles are equal to: ___180_____ degrees ____180____ degrees Triangle 3 interior angles are equal to: Triangle 4 interior angles are equal to: _____180____ degrees _____180____ degrees Step 2: For any triangle, the sum of the interior angles is equal to: ___180 degrees______ © 2016 MathGeekMama.com Exterior Angles of Triangles Step 2: Think About It… Answer Key 1. How do the two interior angles compare to the exterior angle? ______The two interior angles are equal to the exterior angle.__________________________________________________________ 2. Do you think this is true for any triangle? Why? ________Yes, because the 3 interior angles equal 180o and the adjacent interior and exterior equal 180o. Therefore, the two interior angles and the exterior angle are equal to 180o – the those angles._________ 3. Can you write a mathematical formula for the measure of the exterior angle? _Variables used here may vary, but it should be something like d = a + b, where d is the exterior angle and a and b are the opposite interior angles. ._ Step 3: Solve it. Find the measure of the angles indicated below. b 60o c 15o a 90o a = ____150o____ 135o 115o b = ______20o_____ © 2016 MathGeekMama.com 80o c = ____95o____ Thank You! This resource was made possible thanks to the clipart and fonts from these shops: https://www.teacherspayteachers.com/Store/Krista-Wallden https://www.teacherspayteachers.com/Store/Kimberly-Geswein-Fonts http://brittneymurphydesign.com/ Connect with Me: Website: www.MathGeekMama.com FB: https://www.facebook.com/mathgeekmama/ Pin: https://www.pinterest.com/mathgeekmama/ T/IG: @mathgeekmama