Question

Help me with this question please

Answer 1

Reason 1: Given

• We are provided this information through the figure. The red hash marks on both corresponding sides indicate they are congruent segments.

Reason 2: Given

• Angle T and U are marked with the same angle measure red symbols, indicating they are congruent, corresponding angles.

Reason 3: Given

• Segment QT is parallel to RU, which is given at the top of question.

Reason 4: Corresponding Angles Theorem

• Because segment QT is parallel to RU, segment SQ forms a transversal. When a pair of parallel lines is intersected by a transversal, angle relationships are formed for which properties exist. In this case, the corresponding angles are congruent. This will help us prove the two triangles congruent.

Reason 5: Angle-Side-Angle (ASA)

• Lastly, we have a pair of corresponding congruent angles, a pair of corresponding congruent sides, and another pair of corresponding congruent angles. This means we can apply the ASA postulate, which states that if a pair of corresponding angles, a pair of corresponding sides, and another pair of corresponding angles are congruent, then the two triangles are congruent.

I hope this helps!

Answer 2

Explanation:

You just have to recall those rules in geometry. :/

for 1 RU = QT

the red single marks on the segment mean those are the same length

for 2 ∠T = ∠U

the red arc means they are the same angle

for 3 QT is parallel to RU

because of both red marks, same length, and same angles

for 4 RQT = SRU

because both of these angles come from the same line, and have the same length and angle below

for 5 triangle QRT = RSU

because of both red marks and starting from the same line.