Question

8 finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons! given: $\triangle xwz$ is isosceles, $xy\cong zy$ prove: wy bisects $\angle xwz$ $\triangle xwy\cong\triangle zwy$ $\triangle xwz$ is isosceles, $xy = zy$ $\angle yxw=\angle yzw$ wy bisects $\angle xwz$ $\angle xwy=\angle zwy$ $xw = zw$ definition of isosceles given reflexive property asa cpctc sas definition of bisect

Explanation:

Step1: First statement and reason

Statement: $\triangle XWZ$ is isosceles, $XY\cong ZY$
Reason: Given

Step2: Second statement and reason

Statement: $XW = ZW$
Reason: Definition of Isosceles (in an isosceles triangle, the two equal - side lengths are equal)

Step3: Third statement and reason

Statement: $WY = WY$
Reason: Reflexive Property ($a=a$ for any segment $a$)

Step4: Fourth statement and reason

Statement: $\triangle XWY\cong\triangle ZWY$
Reason: $SAS$ (Side - Angle - Side: $XW = ZW$, $XY = ZY$, $WY=WY$)

Step5: Fifth statement and reason

Statement: $\angle XWY\cong\angle ZWY$
Reason: $CPCTC$ (Corresponding Parts of Congruent Triangles are Congruent)

Step6: Sixth statement and reason

Statement: $WY$ bisects $\angle XWZ$
Reason: Definition of Bisect (if $\angle XWY\cong\angle ZWY$, then $WY$ is the bisector of $\angle XWZ$)

Answer:

Statement	Reason
2. $XW = ZW$	2. Definition of Isosceles
3. $WY = WY$	3. Reflexive Property
4. $\triangle XWY\cong\triangle ZWY$	4. $SAS$
5. $\angle XWY\cong\angle ZWY$	5. $CPCTC$
6. $WY$ bisects $\angle XWZ$	6. Definition of Bisect