23) The proof that ΔRSU is congruent to ΔTUS is from; SAS Congruency theorem.
18) The proof that ΔHOW and ΔNEW are congruent is from; SAS congruency theorem.
What are congruent triangles?
23) We are given a rectangle RSTU with diagonal US.
Now, we are told that;
UR is parallel to ST
∠R and ∠T are right angles
We can say that for ΔRSU and ΔTUS, that US is equal to itself in both cases by the reflexive property of congruence.
Now, since ∠R and ∠T are right angles, it means that UR is equal to ST.
Thus for the two triangles;
UR = ST
US = US
∠R = ∠T
There are two corresponding equal sides and one corresponding equal angle and as such, ΔRSU and ΔTUS are congruent by SAS congruency postulate.
18) We are given that;
H O = EN
HW = NW
Now, since HN intersects OE at W, then we can say that;
∠HWO = ∠NWE (Alternate angles)
There are two corresponding equal sides and one corresponding equal angle and as such, ΔHOW and ΔNEW are congruent by SAS congruency postulate.
Read more about Congruent Triangles at; https://brainly.com/question/1675117
