There are two triangles. For the first triangle, the vertices are A, B and C. m<A =65 degrees, m<B=70 degrees and BC = 8. The
second triangle has the vertices E, F and D. m<F = 65 degrees and m<D = 45 degrees. DE = 8. Are the two triangles congruent
and if yes, how do you know? Which segment is congruent to AB (1 point)
No, the triangles are not congruent
O Yes by ASA; EF
• Yes by SAS; EF
• Yes by SAS, ED
• Yes by ASA; ED
The correct answer is: No, the triangles are not congruent.
Find the value of x. The diagram is not to scale.
S
R
T
Given: RS = ST, m/RST = 8x - 60, mLSTU = 10x
(1 point)
O 10°
O 30°
О 22°
0 14°
To find the value of x, we can set up an equation using the information given:
m/RST = 8x - 60
m/LSTU = 10x
Since RS = ST, we can conclude that RST is an isosceles triangle. In an isosceles triangle, the two base angles (angles opposite the equal sides) are congruent. Therefore, we have:
8x - 60 = 10x
Simplifying the equation:
-60 = 2x
x = -30
However, since we are looking for the value of x for an angle measure, it cannot be negative. Therefore, there is no valid value of x in this case.
To determine if two triangles are congruent, we need to compare their corresponding sides and angles.
In the given problem, we have two triangles: ABC and EFD. Let's analyze their angles and sides:
Triangle ABC:
- Angle A measures 65 degrees
- Angle B measures 70 degrees
- Side BC measures 8 units
Triangle EFD:
- Angle F measures 65 degrees
- Angle D measures 45 degrees
- Side DE measures 8 units
To determine if the two triangles are congruent, we can use either the ASA (Angle-Side-Angle) or SAS (Side-Angle-Side) congruence criteria.
Let's check if the triangles are congruent using the ASA criterion:
- The two triangles share an angle with equal measures (both have an angle of 65 degrees).
- The two triangles have sides that are not congruent (BC is not congruent to DE).
Therefore, based on the ASA criterion, the two triangles ABC and EFD are not congruent.
Now, the question asks which segment is congruent to segment AB. Since the two triangles are not congruent, there is no segment in the second triangle that is congruent to AB.