Question

for exercises 5 - 9, sketch and label the figure. mark the figures.

1. isosceles acute triangle act with ac = ct
2. scalene triangle scl with angle bisector $overline{cm}$
3. isosceles right triangle car with $mangle cra = 90^{circ}$
4. two different isosceles triangles with perimeter $4a + b$

Explanation:

Step1: Sketch isosceles acute - triangle ACT

Draw a triangle ACT where AC and CT are of equal length and all angles are acute. Mark AC = CT.

Step2: Sketch scalene triangle SCL with angle - bisector

Draw a triangle SCL with no equal sides. Then draw a line CM that divides one of the angles of triangle SCL into two equal angles. Mark the angle - bisector $\overline{CM}$.

Step3: Sketch isosceles right - triangle CAR

Draw a triangle CAR where $\angle CRA = 90^{\circ}$ and the two legs (the sides adjacent to the right - angle) are of equal length. Mark $\angle CRA=90^{\circ}$.

Step4: Sketch two different isosceles triangles with perimeter

For an isosceles triangle with perimeter $4a + b$, assume the equal sides have length $x$ and the non - equal side has length $y$. So $2x + y=4a + b$. For the first triangle, we can choose $x = a$ and $y = 2a + b$. For the second triangle, we can choose $x = 2a$ and $y=b$. Then draw the two different isosceles triangles with the appropriate side lengths.

Answer:

Sketch and label the figures as described above.