Final answer:
To prove that AWYX = AWZX, we can use the property of a bisector. Since YXZXWX bisects ZYXZ, it divides the two triangles ZYX and ZWX into equal parts. Using the angle-side-angle congruence property, we can conclude that the two triangles AWYX and AWZX are congruent. Congruent triangles have the property that their corresponding sides are equal. Therefore, AWYX = AWZX.
Step-by-step explanation:
To prove that AWYX = AWZX, we can use the property of a bisector. Since YXZXWX bisects ZYXZ, it divides the two triangles ZYX and ZWX into equal parts. Let's label the points where the bisector intersects the sides of the triangle: YXZXWX bisects ZYX at point A and ZWX at point A'.
Now, let's consider the triangles AWYX and AWZX. Since YXZXWX bisects both triangles, we know that angle YAW = angle ZAW and angle YWX = angle ZWX because corresponding angles are congruent. Additionally, the side AW is shared by both triangles. Using the angle-side-angle (ASA) congruence property, we can conclude that the two triangles AWYX and AWZX are congruent.
Congruent triangles have the property that their corresponding sides are equal. Therefore, by congruence, we can say that AWYX = AWZX.