You have two triangles, ADC and ABC.
Sides AD and AB are congruent.
Sides DC and BC are congruent.
Side AC is congruent to itself.
By SSS, triangles ADC and ABC are congruent.
Corresponding parts of congruent triangles are congruent.
That means that angles DAC and BAC are congruent.
Angles DCA and BCA are congruent.
Since m<DAC = 32, then m<BAC = 32
Since m<DCA = 41, then m<BCA = 41.
Now you know the measures of two angles of triangle ABC.
The measures of the interior angles of a triangle add to 180.
You can find the measure of angle B.
m<BAC + m<B + m<BCA = 180
32 + m<B + 41 = 180
m<B + 73 = 180
m<B = 107
Answer:
the answer is a
Step-by-step explanation:
i took the test on gogo.net
Answer:
Yes, the shapes are similar. Note, the angles are equivalent and the sides are scales of each other satisfying the requirements for similarly.
Step-by-step explanation:
For a shape to be similar there are two conditions that must be met. (1) Must have equivalent angles (2) Sides must be related by a scalar.
In the two triangles presented, the first condition is met since each triangle has three angles, 90-53-37.
To test if the sides are scalar, each side must be related to a corresponding side of the other triangle with the same scalar.
9/6 = 3/2
12/8 = 3/2
15/10 = 3/2
Alternatively:
6/9 = 2/3
8/12 = 2/3
10/15 = 2/3
Since the relationship of the sides is the scalar 3/2 (Alternatively 2/3), then we can say the triangles meet the second condition.
Given that both conditions are satisfied, then we can say these triangles are similar.
Note, this is a "special case" right triangle commonly referred to as a 3-4-5 right triangle.
Cheers.
