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# Isosceles Triangle Exploration

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Classroom notes for 8th grade pre-algebra class.

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### Isosceles Triangle Exploration

1. 1. Isosceles Triangle A B C
2. 2. Isosceles Triangle with a Perpendicular Bisector A B C D
3. 3. Isosceles Triangle with a Perpendicular Bisector A B C D
4. 4. Isosceles Triangle with a Perpendicular Bisector Congruent side markings Perpendicular angle markings A B C D
5. 5. Isosceles Triangle with a Perpendicular Bisector Congruent side markings Perpendicular angle markings What else do we know? A B C D
6. 6. Isosceles Triangle with a Perpendicular Bisector <ul><li>What else do we know? </li></ul><ul><ul><li>perpendicular bisector </li></ul></ul>A B C D
7. 7. Isosceles Triangle with a Perpendicular Bisector <ul><li>What else do we know? </li></ul><ul><ul><li>perpendicular bisector </li></ul></ul><ul><ul><li>side congruent to itself </li></ul></ul>A B C D
8. 8. Isosceles Triangle with a Perpendicular Bisector <ul><li>What else do we know? </li></ul><ul><ul><li>perpendicular bisector </li></ul></ul><ul><ul><li>side congruent to itself </li></ul></ul><ul><ul><li>all sides are congruent so Δ ABD= Δ ACD! </li></ul></ul>A B C D
9. 9. Isosceles Triangle with a Perpendicular Bisector If the two triangles are congruent, what else do we know? A B C D
10. 10. Isosceles Triangle with a Perpendicular Bisector If the two triangles are congruent, what else do we know? <A = <C <BAD = <CAD All of its parts, angles and sides are congruent! A B C D
11. 11. Isosceles Triangle with a Perpendicular Bisector A B C D You’ve used geometric reasoning to figure out more information about Δ ABC and its bisector !