Isosceles Triangles 4-3A What makes an isosceles unique? What is an auxiliary line?

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Presentation transcript:

Isosceles Triangles 4-3A What makes an isosceles unique? What is an auxiliary line?

Isosceles Triangles Parts leg base Base angles vertex Vertex angle

The Isosceles Have It! An isosceles triangle has been drawn on a piece of paper and then cut out. (How do you draw an isosceles triangle on a piece of paper?) If the triangle is folded in half, what can be said about the base angles? What can be said about the sides?

Try It What else must be true? 3x+84x−10 MN O

Isosceles Triangle Theorem If two side of a triangle are congruent, then the angles opposite those sides are congruent. Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Unique Bisector Theorems Every segment has a unique midpoint. Every angle has a unique ray that bisects it.

Auxiliary Line The auxiliary lights came on when the power went out. The ladies auxiliary made blankets for the homeless shelter. Auxiliary line is a line (or part of a line) added to a figure. You can add lines and points to a figure as long as you can show that they actually exist.

Proof Statements Reasons 1.Every Segment has unique midpt 2.Two pts determine line 3. Def of midpt 4. Reflexive 5. Given 6. SSS 7. CPCTC XY Z M

What makes an isosceles unique? An isosceles triangle has two congruent sides and two congruent base angles. What is an auxiliary line? Auxiliary line is a line (or part of a line) added to a figure.

Assignment 4-3A Page 289, 1-9, 13, 21-24