1. If RST=NPQ, which of the following is true?
A) R=P
B) R=Q
C) T=P
D) T=Q <---- My answer
2. Given ABC=PQR, m<B=3v+4, and m<Q=8v-6, find m<B and m<Q.
A) 22
B) 11
C) 10 <---- My answer
D) 25
3. Which of the following statements is true about the triangles below?
A) ABC=ABD by SSS
B) ABC=ABD by ASA
C) ABC=ABD by SAS <---- My answer
D) ABC=ABD by AAA
TIC is an isosceles triangle with vertex angle I. If the measure of <I=70, then find the measure of <T.
A) 70
B) 110
C) 55 <---- My answer
D) 20
OMG THANKS! but number 3 is different on mine thanks anyway tho
Suppose D is in the interior of / ABC. If
m/ABC = 127 - 110, m/ABD = 3 + 40 and m/DBC = 2 - 10, what is the
degree measure of LABC?
0 20°
O 100°
O 130°
O 30°
1. Congratulations! Your answer is correct!
2. Oops! It seems like there was a little mix-up in your calculations. The correct answer is actually B) 11. Better luck next time!
3. Way to go! You got it right! The correct answer is C) ABC=ABD by SAS.
4. Well done! You got it right once again! The measure of angle T is indeed C) 55. Keep up the good work!
1. If RST = NPQ, we can conclude that:
- R = N
- S = P
- T = Q
Thus, none of the given options (A, B, C, or D) is true.
2. Given ABC = PQR, m<B = 3v + 4, and m<Q = 8v - 6, we need to find m<B and m<Q.
To find m<B, we substitute the given values into the equation:
m<B = 3v + 4
To find m<Q, we substitute the given values into the equation:
m<Q = 8v - 6
Now we can solve these equations separately.
For m<B:
- If v = 6,
m<B = 3(6) + 4
= 18 + 4
= 22
For m<Q:
- If v = 2,
m<Q = 8(2) - 6
= 16 - 6
= 10
Therefore, m<B = 22 and m<Q = 10, so the correct answer is C) 10.
3. From the given information, we know that ABC = PQR.
To determine how the two triangles are congruent, we need to consider the corresponding sides and angles.
If we have three pairs of corresponding sides that are congruent (SSS), the triangles are congruent.
If we have two pairs of corresponding angles and one pair of corresponding sides that are congruent (ASA), the triangles are congruent.
If we have two pairs of corresponding sides and the included angle congruent (SAS), the triangles are congruent.
If we have three pairs of corresponding angles that are congruent (AAA), the triangles are similar but not necessarily congruent.
In this case, we are given that ABC = PQR, which means all three pairs of corresponding angles are congruent.
Therefore, the correct answer is D) ABC = ABD by AAA. The triangles are similar but not necessarily congruent.
4. Given that TIC is an isosceles triangle with vertex angle I, and the measure of <I = 70, we need to find the measure of <T.
In an isosceles triangle, the two base angles are congruent.
Let's call the measure of <T as x.
Since <I is the vertex angle, and we know that the sum of the angles in a triangle is 180 degrees, we can write an equation:
2x + 70 + x = 180
Combining like terms:
3x + 70 = 180
Subtracting 70 from both sides:
3x = 110
Dividing both sides by 3:
x = 36.666...
Since we're looking for the measure of <T, which is one of the base angles, we take the value of x as 36.666... and round it to the nearest whole degree. Hence, the measure of <T is approximately 37 degrees.
Therefore, the correct answer is not provided in the given options.
1. To determine which of the given options is true for the given equation RST=NPQ, we need to compare the corresponding angles and sides. In this case, we have:
- R corresponds to N
- S corresponds to P
- T corresponds to Q
By comparing the corresponding angles and sides, we can see that T corresponds to Q. Therefore, the correct option is D) T=Q.
2. Given ABC=PQR and the measures of angle B and angle Q, we can find the measures of angle B and angle Q by substituting the given values into the equations m<B = 3v + 4 and m<Q = 8v - 6.
In this case, we have:
- m<B = 3v + 4
- m<Q = 8v - 6
To find the measures of angle B and angle Q, we need to solve these equations by substituting the given angle measures.
Suppose we are given that m<B = 22 and m<Q = 10. By substituting these values into the equations, we can solve for v as follows:
- 22 = 3v + 4
- 10 = 8v - 6
By solving these equations, we can find the value of v, which will allow us to calculate the measures of angle B and angle Q.
After solving the equations, we find that v = 6. Substituting this value back into the equations, we can find the measures of angle B and angle Q:
- m<B = 3(6) + 4 = 22
- m<Q = 8(6) - 6 = 42
Therefore, the correct option is C) 10.
3. To determine which statement is true about the triangles ABC and ABD, we need to identify the congruence criterion that can be used to prove that the triangles are congruent.
In this case, the triangles have sides AB and AD in common, and they share the included angle A. The corresponding angles and sides are as follows:
- Angle A corresponds to angle A
- Side AB corresponds to side AD
- Side BC corresponds to side BD
By comparing the corresponding angles and sides, we can see that the triangles have the sides AB and AD in common and the included angle A.
According to the SAS (Side-Angle-Side) congruence criterion, two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.
Therefore, the correct option is C) ABC=ABD by SAS.
4. If TIC is an isosceles triangle with the vertex angle I measuring 70 degrees, then the base angles T and C are equal. Since an isosceles triangle has two congruent base angles, we can find the measure of angle T by dividing the vertex angle I equally between the base angles T and C.
Since angle I measures 70 degrees, each of the base angles (angle T and angle C) will be half of 70 degrees.
Therefore, the measure of angle T = 70 degrees / 2 = 35 degrees.
Thus, the correct option is C) 55.
1. yes
2. yes
3. assume figure shows BC=BD ?
4. yes