Question

draw a triangle with the given description. (section 7.3)

1. a triangle with angle measures of 35°, 65°, and 80°
2. a triangle with a 5 - centimeter side and a 7 - centimeter side that meet at a 70° angle
3. an obtuse scalene triangle

Explanation:

For 8:

First confirm the angle sum: $35^\circ + 65^\circ + 80^\circ = 180^\circ$, which is valid for a triangle. Draw any triangle where the three interior angles match these values (sides can be any length, as it's an acute scalene triangle).

For 9:

Draw a $70^\circ$ angle. Mark 5 cm on one ray and 7 cm on the other ray, then connect the endpoints of the two segments to form the triangle.

For 10:

Draw a triangle with one angle greater than $90^\circ$ (obtuse) and all three sides of different lengths (scalene, so no equal sides/angles).

Answer:

1. For the triangle with angles $35^\circ$, $65^\circ$, $80^\circ$: Draw an acute scalene triangle with the three specified interior angles.
2. For the triangle with 5-cm, 7-cm sides meeting at $70^\circ$: Construct a $70^\circ$ angle, mark 5 cm and 7 cm on its rays, then connect the segment endpoints.
3. For the obtuse scalene triangle: Draw a triangle with one angle $>90^\circ$ and all three sides of distinct lengths.