Exercise 9 Page 340

An acute triangle is a triangle where all angles are less than $90^{\circ }.$ The triangle is also scalene which means no sides and no angles are congruent.

Let's start by drawing an arbitrary side of the triangle using a ruler. We will make it $6$ cm long.

Next, we will use a protractor to measure one of the triangles angles. Since we want this to be an acute triangle, we will have to choose an angle that's between $0^{\circ }$ and $90^{\circ }.$ Let's go with $80^{\circ }.$

Let's measure one more angle. Note that we cannot make it $80^{\circ }$ as we then would end up with an isosceles triangle. We also have to avoid $50^{\circ }$ as well because this would also make our triangle isosceles since $80^{\circ }+50^{\circ }+50^{\circ }=180^{\circ }.$ Let's choose $40^{\circ }.$

Let's draw the remaining sides using our red markings and a ruler for a straightedge.

Finally, we will clean up the diagram and mark the longest and shortest sides as well as the angle with the largest and smallest measure.

Examining the diagram, we notice that the shortest side is opposite the smallest angle and the longest side is opposite the largest angle.