Question

In triangle RST, mZR > mZS + mZT. Which must be true of triangle RST? Check all that apply.

a) mZR > 90°
b) mZS + mZT < 90°
c) mZS = mZT
d) mZR > mZT
e) mZR > m_S
f) mZS > mZT

Answer 1

The properties of triangle RST based on the given angle information are that mZR is greater than 90°, mZR is greater than mZS, and mZR is greater than mZT.

Step-by-step explanation:

The student's question asks about the properties of triangle angles in the context of triangle RST where the measure of angle R (mZR) is described as being greater than the sum of the measures of angle S (mZS) and angle T (mZT).

From the given information, mZR > mZS + mZT, we can infer certain properties:

• mZR > 90°, because the sum of the other two angles has to be less than 90° for mZR to be larger than their sum (the sum of all angles in a triangle is 180°).
• mZR > mZT and mZR > mZS individually, as mZR is greater than the sum of the other two angles, it must be greater than each one individually.

Therefore, the true statements about triangle RST are: (a) mZR > 90°, (d) mZR > mZT, and (e) mZR > mZS. The remaining options cannot be confirmed with the given information. Statement (c) mZS = mZT and (f) mZS > mZT are not necessarily true, and (b) mZS + mZT < 90° can be inferred as true since mZR is greater than their sum.