+327 32)
The measure of side BC=
A: \(n\)
B: \(n\sqrt{2}\)
C: \(\sqrt{2}\)
D: \(\frac{n\sqrt{2}}{2}\)
40) You are given two triangles and the information that the three pairs of corresponding angles are congruent. What other information would guarantee that the triangles are congruent?
A: The triangles are right.
B: All corresponding sides are proportional.
C: One pair of corresponding sides is proportional.
D: One pair of corresponding sides has the same measure.
43)
If minor arc AC = 96°, what is the measure of ∠ABC?
A: 53°
B: 64°
C: 72°
D: 84°
Please Help Me With These Last Three Questions!!!
+9479 32)
Since the sum of the angle measures in every triangle is 180°,
and we know that two of the angles are 90° and 45°.....
the measure of the third angle = m∠A = 180° - 90° - 45° = 45°
Since m∠A = m∠C , triangle ABC is isosceles and AB = BC
By the Pythagorean Theorem...
(AB)2 + (BC)2 = n2
We can replace AB with BC since they are the same length.
(BC)2 + (BC)2 = n2
Combine like terms.
2(BC)2 = n2
Divide both sides of the equation by 2 .
(BC)2 = n2 / 2
Take the positive square root of both sides.
BC = \(\sqrt{\frac{n^2}{2}}\)
Simplify.
BC = \(\frac{\sqrt{n^2}}{\sqrt2}\)
BC = \(\frac{n}{\sqrt2}\)
Rationalize denominator.
BC = \(\frac{n\sqrt2}{2}\)
+9479 40)
You are given two triangles and the information that the three pairs of corresponding angles are congruent. What other information would guarantee that the triangles are congruent?
D: One pair of corresponding sides has the same measure.
43)
If minor arc AC = 96°, what is the measure of ∠ABC?
Here's how I have to think of these....
Draw the angle that forms minor arc AC...its measure is 96° .
Even though it wasn't specifically stated in the question, I assume that lines AB and BC are tangent to the circle. That means line AB and line BC each forms a right angle with the line drawn from the center of the circle to point A and point C respectively.
The sum of the angle measures in every quadrilateral is 360° . So....
m∠ABC = 360° - 90° - 90° - 96° = 180° - 96° = 84°
