Question

Help with this question Asap!! I need all the help I can get!

Answer 1

`\large{YES}\ (BC)/(YZ)=(AC)/(XY)=(AB)/(XZ)=(2)/(1)\\\\\text{and}\ \angle B\cong\angle Z,\ \angle C\cong\angle Y,\ \angle A\cong\angle X`

Explanation:

`BC\to ZY\\AB\to XZ\\AC\to XY\\\angle A\to\angle X\\\angle B\to\angle Z\\\angle C\to\angle Y`

`\text{We have:}\\\\\triangle ABC:\ AB=20,\ BC=12,\ AC=18\\\triangle XZY:\ XZ=10,\ YZ=6,\ XY=9\\\\\text{check the ratio:}\\\\(AB)/(XZ)=(20)/(10)=2\\\\(BC)/(YZ)=(12)/(6)=2\\\\(AC)/(XY)=(18)/(9)=2\\\\\text{CORRECT :)}\\\\\angle B\cong\angle Z,\ \angle C\cong\angle Y\\\\\text{We know that: The sum of the acute angles in a right triangle is}\ 90^o.\\\\m\angle B+m\angle A=90^o\ \text{and}\ m\angle Z+m\angle X=90^o`

`\text{We know}\ m\angle B=m\angle Z\to \ m\angle A=m\angle X.\\\text{therefore}\ \angle A\cong\angle X`