UNIT 4 LESSON 2: ISOSCELES TRIANGLES THEOREMS

THEOREMS AND COROLLARIES OF ISOSCELES TRIANGLES

COROLLARY: A theorem that follows on from another theorem. Example: there is a Theorem that says: two angles that together form a straight line are "supplementary" (they add to 180°). A Corollary to this is the "Vertical Angle Theorem" that says: where two lines intersect, the angles opposite each other are equal (a=c and b=d in the diagram).

Definition: An ISOSCELES TRIANGLE is a triangle that has AT LEAST 1 PAIR OF CONGRUENT SIDES. MUST USE APPLET IN FULL SCREEN Directions: 1) Click on the red checkbox to illustrate this definition. 2) Move any 1 (or more) of the vertices of this triangle around. Does it remain isosceles? 3) Click on checkbox 2. Move the vertices of the triangle around again. What do you notice? 4) Click on checkbox 3. This will draw the line that bisects the vertex angle of the isosceles triangle. 5) Click on checkbox 4. What else do you notice? 6) Please answer the questions that appear below this applet.

Fill in the following blanks (based upon your observations). The words to complete these statements can be found in the word bank below. 1) If two sides of a triangle are congruent, then the _____________________ opposite those sides are ____________________. Word Bank: bisector angles congruent perpendicular vertex bisector

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Fill in the following blanks (based upon your observations). The words to complete these statements can be found in the word bank below. 2) The ___________________ of the _________________ angle of an isosceles triangle is the ________________________ ________________ of the base (3rd side). Word Bank: bisector angles congruent perpendicular vertex bisector

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I adjusted point D so the measure of angle BAD is equal to the measure of angle CAD. Which statements are true? Check all that apply. -------------------------------------->

Select all that apply