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Transcript

Name____________________________ Date_____________ Proving Triangles Congruent Congruent Sides In this activity, you will examine whether S (side), SS (side-side) and/or SSS (side-side-side) guarantee triangle congruence. 1. Under Conditions, select S. a. Name the pair of sides in the triangles that are congruent. ________________ b. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? ________________________ c. Click on Click to measure lengths and use the interactive rulers to measure the lengths of AB and DE ; BC and EF ; AC and DF . Write the lengths here. _______________________________________________________________ d. Are all the pairs of sides always congruent?____________________________ e. Does having one pair of sides congruent guarantee that two triangles are congruent? Explain your answer. ___________________________________ _______________________________________________________________ 2. Under Conditions, select SS. a. Name the pairs of sides in the triangles that are congruent. __________________ b. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? ___________________________ c. Click on Click to measure lengths and use the interactive rulers to measure the lengths of AB and DE ; BC and EF ; AC and DF . Write the lengths here. _______________________________________________________________ d. Are all pairs of sides always congruent?_______________________________ e. Does having two pairs of sides congruent guarantee that two triangles are congruent? Explain your answer. ______________________________________ ___________________________________________________________________ 3. Under Conditions, select SSS. a. Name the pairs of sides in the triangles that are congruent. __________________ b. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? ___________________________ c. Click on Click to measure lengths and use the interactive rulers to measure the length of AB and DE ; BC and EF ; AC and DF . Write the lengths here. _______________________________________________________________ d. Are all pairs of sides always congruent? _______________________________ e. Does having three pairs of sides congruent guarantee that two triangles are congruent? Explain your answer. ______________________________________ ___________________________________________________________________ Congruent Sides and Angles In this activity, you will examine whether the conditions SA (side-angle), SAS (side-angle-side), and/or ASA (angle-side-angle) guarantee triangle congruence. 4. Under Conditions, select SA. a. Name the pair of sides and the pair of angles that are congruent. ______________ b. What does adjacent mean? ____________________________________________ c. Name another angle that is adjacent to each of the congruent sides. ___________ d. Are those angles congruent? Click on Click to measure angles and use the interactive protractors to measure the angles. mA _____; mD ______; mB ______; mE ______; mC ______; mF _______ e. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? __________________________________________ f. Does having one pair of sides and a pair of adjacent angles congruent guarantee congruent triangles? Explain your answer. ________________________________ ___________________________________________________________________ 5. Under Conditions, select SAS. a. Name the pairs of sides and the pair of angles that are congruent. ___________________________________________________________________ b. In the top triangle, which angle is included between and ? What is the difference between adjacent and included?________________________________ ___________________________________________________________________ c. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? __________________________________________ d. Does having two pair of sides and the corresponding pair of included angles congruent guarantee congruent triangles always, sometimes or never? Explain your answer. _______________________________________________________ ___________________________________________________________________ 6. Under Conditions, select ASA. a. Name the pair of sides and the pairs of angles that are congruent. ___________________________________________________________________ b. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? _________________________________________ c. Does having two pairs of angles and the corresponding pair of included sides congruent guarantee congruent triangles always, sometimes or never? Explain your answer. _______________________________________________________ __________________________________________________________________ Congruent Angles In this activity, you will explore whether A (angle), AA (angle-angle), and/or AAA (angle-angle-angle) guarantees triangle congruence. 7. Under Conditions, select A. a. Name the pair of angles in the triangles that are congruent. ________________ b. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? ________________________ c. Click on Click to measure angles and use the interactive protractors to find the measures A of D and ; B and E ; C and F . Write the measures here. mA _____; mD ______; mB ______; mE ______; mC ______; mF _______ d. Are all the pairs of angles always congruent? ___________________________ e. Does having one pair of angles congruent guarantee that two triangles are congruent? Explain your answer. ___________________________________ _______________________________________________________________ 8. Under Conditions, select AA. a. Name the pairs of angles in the triangles that are congruent. __________________ b. Drag the vertices of the triangles to form new triangles. Can you make triangles that are not congruent? ___________________________ c. Click on Click to measure lengths and use the interactive rulers to measure the lengths of AB and DE ; BC and EF ; AC and DF . Write the lengths here. _______________________________________________________________ d. Does having two pairs of angles congruent guarantee that two triangles are congruent? Explain your answer. _______________________________________ __________________________________________________________________ e. If two pairs of angles are congruent, what can you conclude about the third pair of angles?_________________________________________________________ 9. Once you have tested AA (angle-angle) to see if it guarantees that two triangles are congruent, there is no reason to test AAA (angle-angle-angle) because it is exactly the same as AA. Explain why this is true. _________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 10. Which conditions CAN ALWAYS PROVE two triangles congruent? Circle your answers. A AA AAA S SS SSS SA SAS ASA SAA SSA