Answer:
Explanation:
Exercise 2:
1.To construct the triangle ABC, start by drawing a line segment BC of length 5cm. Using a protractor, measure and mark an angle of 80° at B and an angle of 40° at C. Connect the two marked angles with a line to form triangle ABC.
2.The bisector of angle ABC cuts the line segment AC at M.
a. To calculate MBC, we can use the Angle Bisector Theorem, which states that the ratio of the lengths of the bisector of a given angle of a triangle to the sides of the triangle is equal to the ratio of the other two sides of the triangle. So, MBC/AC = BC/AB. Since angle B=80° and angle C=40°, angle A is (180-(80+40))=60°. Therefore, AB/BC = MC/MB.
b. Using the Angle Bisector Theorem again, we can see that MBC/AC = BC/AB, which means that MBC/5 = 5/AB. And since AB/BC = MC/MB, we can deduce that MB = MC. Therefore, triangle MBC is an isosceles triangle.
c. As we know that MB=MC, we can say that triangle MBC is an isosceles triangle.
Note: To construct the triangle in a more accurate way, you may need a ruler and a compass, and the angles and sides should be measured and drawn with more precision.