Question

1. 16) 17) 18) sketch an example of the type of triangle described. mark the triangle to indicate what information is known. if no triangle can be drawn, write

ot possible.\ 19) acute isosceles 20) right scalene 21) right isosceles 22) right equilateral 23) acute scalene 24) obtuse scalene 25) right obtuse 26) equilateral

Explanation:

Step1: Recall triangle - type definitions

An acute - angled triangle has all angles less than 90°. An isosceles triangle has two equal sides. A right - angled triangle has one angle equal to 90°. A scalene triangle has all sides of different lengths. An equilateral triangle has all sides equal and all angles equal to 60°. An obtuse - angled triangle has one angle greater than 90°.

Step2: Sketch 19) acute isosceles

Draw a triangle with all angles less than 90° and two equal sides. Mark the equal sides with the same number of hash marks.

Step3: Sketch 20) right scalene

Draw a triangle with one 90° angle and all sides of different lengths. Mark the right - angle with a small square and the sides with different numbers of hash marks to show they are unequal.

Step4: Sketch 21) right isosceles

Draw a triangle with one 90° angle and two equal sides. Mark the right - angle with a small square and the equal sides with the same number of hash marks.

Step5: Analyze 22) right equilateral

An equilateral triangle has all angles equal to 60°. A right - angled triangle has one angle equal to 90°. So, a right equilateral triangle is not possible. Write "not possible".

Step6: Sketch 23) acute scalene

Draw a triangle with all angles less than 90° and all sides of different lengths. Mark the sides with different numbers of hash marks.

Step7: Sketch 24) obtuse scalene

Draw a triangle with one angle greater than 90° and all sides of different lengths. Mark the sides with different numbers of hash marks.

Step8: Analyze 25) right obtuse

A right - angled triangle has one angle equal to 90° and an obtuse - angled triangle has one angle greater than 90°. The sum of the interior angles of a triangle is 180°. So, a right obtuse triangle is not possible. Write "not possible".

Step9: Sketch 26) equilateral

Draw a triangle with all sides equal. Mark all sides with the same number of hash marks.

Answer:

1. Sketch an acute - angled triangle with two equal sides.
2. Sketch a right - angled triangle with all sides unequal.
3. Sketch a right - angled triangle with two equal sides.
4. not possible
5. Sketch an acute - angled triangle with all sides unequal.
6. Sketch an obtuse - angled triangle with all sides unequal.
7. not possible
8. Sketch an equilateral triangle.