a Follow the instructions you are given in the book.
B
b Use a ruler to measure the given leg lengths, then add all side lengths to evaluate the perimeter of each triangle .
C
c What can you say about the change in the perimeter, looking at the table you made in Part B?
A
a See solution.
B
b See solution.
C
c If the leg length of an isosceles triangle is increased or decreased by a factor, keeping the same vertex angle, then the perimeter of the triangle increases or decreases by the same factor.
Practice makes perfect
a Let's start with drawing an isosceles triangle and drawing its base AC.
Now, we will construct a line perpendicular to this side and passing through its midpoint. To do this, we will place the compass at each of the endpoints of this segment and draw arcs above and below this segment using a setting greater than half of the segment's length.
Next, we will connect the points of intersection of the arcs with a line. This line contains a height of this triangle since the height in isosceles triangles bisects the base.
With this, we can choose any point that lies on this line to be the third vertex of this triangle. Let's label it B.
Finally, we will connect the points to form a triangle.
Next, we will measure and label the legs and the vertex angle. Let's use a ruler.
Now, using a protractor, we will measure the vertex angle.
We can draw the triangles MNO and PQR in the same way. Remember to keep the same vertex angle. The second triangle will have legs twice as long as â–łABC and the third triangle will have legs half as long as â–łABC.
b In this part we are asked to complete the given table. To evaluate the perimeters of drawn triangles, we need to measure the base of each of them. Let's use the ruler to do this.
As we know the measures of the appropriate angles, we can complete the given table. Recall that the perimeter of a triangle is a sum of all its sides.
Triangle
ABC
MNO
PQR
Leg Length
5
10
2.5
Perimeter
5+ 5+6=16
10+ 10+12=32
2.5+ 2.5+3=8
c As we can see from the table we made in Part B, the perimeter of MNO is twice the perimeter of ABC, and the perimeter of PQR is half of the perimeter of ABC. P_(MNO)=2* P_(ABC)
P_(PQR)=1/2* P_(ABC)
Therefore, we can assume that if the leg length of an isosceles triangle is increased or decreased by a factor, keeping the same vertex angle, then the perimeter of the triangle increases or decreases by the same factor.
