4-6+Special+Triangles

=__4-6 Special Triangles (Isosceles, Equilateral and Right Triangles) __=  By, Shauna Menzella

====**What do we want to make sure you understand after reading this section?** In this section you will learn the different triangles including isosceles triangles, equilateral triangles, and right triangles. You will also learn the different theorems associated with this triangles including the base angles theorem, the converse of the base angles theorem, and the hypotenuse-leg theorem. You will understand how to label and identify these types of triangles. ====

__Isosceles Triangles __
What is an isosceles triangle? An isosceles triangle is a triangle that has //__**at least**__// **two congruent sides**. It has a vertex angle and two congruent base angles along with a base and two congruent legs.



__Base Angles Theorem __
If two sides of a triangle are congruent, then the angles opposite of them are congruent. If line AB is congruent to line AC then angle B is congruent to angle C

__Converse of the Base Angles Theorem __
If two angles of a triangle are congruent, then the sides opposite them are congruent. If angle B is congruent to Angle C then line AB is congruent to line AC 

__Example: __


Find X and Y. (*Hint: break them into separate triangles and see if that helps!*)
 * __Try It!: __**

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 * <span style="font-family: 'Comic Sans MS',cursive;">Still Confused? Check out these websites: **

<span style="font-family: 'Comic Sans MS',cursive;">__Equilateral Triangles__
<span style="font-family: 'Comic Sans MS',cursive;">What is an equilateral triangle? <span style="font-family: 'Comic Sans MS',cursive;">A triangle where **//__all 3 sides__// are equa<span style="font-family: 'Comic Sans MS',cursive;">l **<span style="font-family: 'Comic Sans MS',cursive;">. All three interior angles __always__ add up to 60 degrees. It is also known as a "special isosceles triangle." <span style="font-family: 'Comic Sans MS',cursive;">If a triangle is equilateral, then it is equiangular. <span style="font-family: 'Comic Sans MS',cursive;">If a triangle is equiangular, then it is equilateral.

<span style="font-family: 'Comic Sans MS',cursive;">__**Right Triangle**__
<span style="font-family: 'Comic Sans MS',cursive;">A triangle with a right angle. It has 2 legs and the other segment opposite from the right angle is called the hypotenuse.



__**<span style="font-family: 'Comic Sans MS',cursive;">Hypotenuse-Leg Congruence Theorem **__
<span style="font-family: 'Comic Sans MS',cursive;">If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. If segment BC is congruent to XY and segment AC is congruent to ZY, then triangle ABD is congruent to triangle ZXY.

//<span style="font-family: 'Comic Sans MS',cursive;">**Remember: Before you think an answer to a proof (when proving two right triangles are congruent) may be A-S-S or S-S-A look again! It's probably just HL!** //

__<span style="font-family: 'Comic Sans MS',cursive;">Try It!: __ <span style="font-family: 'Comic Sans MS',cursive;"> <span style="font-family: 'Comic Sans MS',cursive;">__Still confused? Check out this website:__ <span style="font-family: 'Comic Sans MS',cursive;">[] <span style="font-family: 'Comic Sans MS',cursive;">[]

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<span style="font-family: 'Comic Sans MS',cursive;">__**Answers:**__
<span style="font-family: 'Comic Sans MS',cursive;">__**Base Angle Theorem Problems:**__
 * <span style="font-family: 'Comic Sans MS',cursive;">__First problem__-x=106, y-37
 * <span style="font-family: 'Comic Sans MS',cursive;">__Second problem__- x=62, y=56
 * <span style="font-family: 'Comic Sans MS',cursive;">__Hypotenuse Leg Theorem:__ **
 * <span style="font-family: 'Comic Sans MS',cursive;">W<span style="font-family: 'Comic Sans MS',cursive;">e already know that Line MK is congruent to Line JL and Angle MKL and Angle JKL are equal to 90. So, be definition of a right angle, Angle MKL and Angle JKL are right angles. Since we know that triangle LKJ and MLK are right triangles by the definition of a right triangle. Line KL is congruent to Line KL by the reflexive property. So, using the HL theorem, we can conclude that Triangle LKJ is congruent to Triangle MLK.

<span style="font-family: 'Comic Sans MS',cursive;">__Sources (for pictures):__ <span style="font-family: 'Comic Sans MS',cursive;">[] <span style="font-family: 'Comic Sans MS',cursive;">[] <span style="font-family: 'Comic Sans MS',cursive;">[] <span style="font-family: 'Comic Sans MS',cursive;">[]