Answers
Set 23
- Cannot be a triangle. Since m∠D = m∠B = 47°, then this is an
isosceles triangle with a vertex at ∠E that equals 86° (180°(47°)
(2) = 86°). Since ∠E is the largest angle, it must be opposite the
largest side, but it is opposite the smallest side, 17. Therefore, this
cannot be a triangle. - Cannot be a triangle.Any triangle can have one right angle or
one obtuse angle, not both. “Triangle” QRS claims to have a right
angle and an obtuse angle. - Cannot be a triangle. “Triangle” WXY claims to be equilateral
and right; however, an equilateral triangle also has three congruent
interior angles, and no triangle can have three right angles. - Acute scalene triangle PQR.Subtract from 180° the sum of ∠P
and ∠R. ∠Q measures 60°. All three angles are acute, and all three
angles are different. ΔPQR is acute scalene. - Isosceles right triangle ABD. ∠A is a right angle and sides
AB = AD. - Cannot be a triangle.In triangles, the sum of any two sides of a
triangle must be greater than the length of the remaining third
side. In this case 20 + 24 = 44, which is the length of the third side.
This means the sum of two of the sides of the triangle is equal to
and not greater thanthe remaining side, so ΔTAR cannot exist. - Acute equilateral triangle DEZ.Subtract from 180° the sum of
∠1 and ∠2. ∠3, like ∠1 and ∠2, measures 60°. An equiangular
triangle is an equilateral triangle, and both are always acute. - Scalene right triangle CHI.∠3 is a right angle; ∠1 and ∠2 are
acute; and all three sides have different lengths. - Cannot be a triangle. Add the measurements of each angle
together. The sum exceeds 180° so ΔJMR cannot exist.
501 Geometry Questions