Question

(ASAP!!) Given that point M is the midpoint of TS and UR which of the following triangle congruence methods could be used to prove TUM SRM? T R M U S Do O ASA 0 O AAA O 0 O Qo O SAS 0 O SSS​

Answer 1

Answer: SAS or Side-Angle-Side

Step-by-step explanation: Two triangles are congruent if they have the same exactly 3 sides and same exactly 3 angles.

There are methods to help prove congruence.

For example:

• ASA or Angle-Side-Angle: when two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle;
• SAS or Side-Angle-Side: when two sides and the included angle of one triangle is congruent to the corresponding parts of the other triangle;
• SSS or Side-Side-Side: if three sides of one triangel are congruent to the three sides of the other triangle, they are congruent;

The triangles TUM and SRM are congruent because:

Lines RU and TS intersect at point M forming two pair of opposite angles, which are vertical and therefore, the same.

Being midpoint, point M divides RU into two equal segments: UM = MR. The same happens to TS: TM = MS.

Two sides and the included angle of one triangle is congruent to the corresponding parts of the other triangle, which means ΔTUM and ΔSRM are congruent and proved by SAS method.