Mathematics High School

If PQR ≈ STU complete each part

Answers

Answer 1

*see attachment for the complete diagram and what is required.

Answer:

✅ST = 7 m

✅SU = 8 m

✅m<R = 46°

✅m<Q = 75°

✅m<S = 59°

Step-by-step explanation:

Given that ∆PQR ≅ ∆STU, therefore, their corresponding sides and angles would be congruent to each other.

Thus:

<P ≅ <S, therefore, m<P = m<S = 59°

<Q ≅ <T, therefore, m<Q = m<T = 75°

<R ≅ <U, therefore, m<R = m<U.

PQ ≅ ST, therefore, PQ = ST

QR ≅ TU, therefore, QR = TU

PR ≅ SU, therefore, PR = SU

Let's find the measure of the following with the information we already know:

✅ST = PQ = 7 m

✅SU = PR = 8 m

✅m<R = 180 - (m<P + m<Q) (sum of ∆)

m<R = 180 - (59°+ 75°) (substitution)

m<R = 180 - 134

m<R = 46°

✅m<Q = m<T = 75°

✅m<S = m<P = 59°

Answer 2

The length of the segment ST is 7m, the length of the segment SU is 8m, angle R is 46 degrees, angle Q is 75 degrees, and angle S is 59 degrees.

Given :

PQR ≈ STUThe segment PR = 8 mThe segment PQ = 7 mAngle RPQ is 59 degrees.Angle STU is 75 degrees.

The following steps can be used in order to complete each part:

Step 1 - Angle P is similar to angle P therefore, angle S is 59 degrees.

Step 2 - Angle Q is similar to angle T therefore, angle Q is 75 degrees.

Step 3 - Angle R is similar to angle U therefore, angle R and angle U are equal.

Step 4 - Segment PQ is similar to segment ST, therefore the length of segment PQ is equal to the length of segment ST.

Step 5 - Segment QR is similar to segment TU, therefore the length of segment QR is equal to the length of segment TU.

Step 6 - Segment PR is similar to segment SU, therefore the length of segment PR is equal to the length of segment SU.

Step 7 - Apply the sum of interior angle property on the triangle PQR.

[tex]\rm \angle R + 59 + 75 = 180[/tex]

[tex]\rm \angle R = \angle U = 46^\circ[/tex]

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Answers

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Edge2020

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The correct answer is 8.

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Answers

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