Activity 3.2.3 Sides and Angles in a Triangle Study the two proofs and answer all questions in bold. I. Prove the Angle Opposite Longer Side Theorem: If two sides of a triangle are not equal, the angle opposite the longer side is greater than the angle opposite the shorter side. Given: with > ∆ABC AC AB. Prove: m > m ABC BCA Construct a circle with center passing through point Let be the point where the Step 1. A B. D circle intersects side AC. How can we be sure that point lies between points and D A C? Join points and Step 2. B D. In exterior angle is greater than interior angle Step 3. ADB BCA. ∆BDC What theorem are we using here? = Step 4. AB AD Why? Therefore m m ADB ABD
Activity 3.2.3 Sides and Angles in a Triangle Study the two proofs and answer all questions in bold. I. Prove the Angle Opposite Longer Side Theorem: If two sides of a triangle are not equal, the angle opposite the longer side is greater than the angle opposite the shorter side. Given: ∆ABC with AC > AB. Prove: m ABC > m BCA Step 1. Construct a circle with center A passing through point B. Let D be the point where the circle intersects side AC. How can we be sure that point D lies between points A and C? Step 2. Join points B and D. Step 3. In ∆BDC exterior angle ADB is greater than interior angle BCA. What theorem are we using here? Step 4. AB = AD Why? Therefore m ADB m ABD
Activity_3_2_3.docx