Answers
*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°
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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