Determine whether you can construct many, one, or no triangle(s) with each description.
a)An isosceles triangle with angle measures of 40° and 100°-Many
b)A right triangle with three congruent sides-one
c)A scalene triangle with side lengths of 7 cm, 3 cm, and 9 cm-none
OH for three...
no such thing as an equilateral right triangle
only one way each to make the other two
b)A right triangle with three congruent sides-one
DiS iS iMpOsSiBle
To determine how many triangles can be constructed with each description, we need to consider the rules and properties of triangles.
a) For an isosceles triangle with angle measures of 40° and 100°, we know that the sum of the interior angles of a triangle is always 180°. Since we have one angle of 40° and another angle of 100°, the third angle must be 180° - 40° - 100° = 40°. Because two angles of the triangle are congruent (40° and 40°), the triangle would have two equal sides as well. Therefore, we can construct many isosceles triangles with these angle measures.
b) A right triangle is a triangle with one angle measuring 90°. If the three sides of the triangle are congruent, then the triangle is an equilateral triangle, not a right triangle. So, it is not possible to construct a right triangle with three congruent sides. Therefore, no triangle can be constructed with this description.
c) A scalene triangle is a triangle with all three sides of different lengths. If the given side lengths of a triangle are 7 cm, 3 cm, and 9 cm, we need to check if these lengths satisfy the triangle inequality theorem. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check:
- 7 cm + 3 cm = 10 cm (which is less than 9 cm)
- 3 cm + 9 cm = 12 cm (which is greater than 7 cm)
- 7 cm + 9 cm = 16 cm (which is greater than 3 cm)
Since the sum of the lengths of any two sides is not greater than the length of the third side, it is not possible to construct a triangle with side lengths of 7 cm, 3 cm, and 9 cm. Therefore, no triangle can be constructed with this description.
for A) it is none
for B) it is many
for C) it is one
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