MATH SOLVE

4 months ago

Q:
# △ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?

Accepted Solution

A:

Answer:The correct option is;∠A ≅ ∠A ; reflective propertyStep-by-step explanation:1. ΔABC is isosceles with legs AB and ACΔAYX is also isosceles with legs AY and AX2. AB ≅ AC and AY ≅ AX (Definition of isosceles triangle) 3. AB = AC and AY = AX (Definition of congruency)4. AY · AC = AX · AC (Multiplication property of equality)5. AY · AC = AX · AB (Substitution property of equality)6. [tex]\dfrac{AC}{AX} = \dfrac{AB}{AY}[/tex] (Division property of equality)7. [tex]\dfrac{AC}{AX} = \dfrac{AB}{AX}[/tex] (Division property of equality)8. ∠A ≅ ∠A ; reflective property9. ΔABC ~ ΔAXY SAS similarity theorem (The two triangles have the same vertex angle A hence they are similar based on the Side Angle Side theorem for uniqueness of triangles.