Chapter 4 exercises
- Author:
- Jorge Cássio
- Topic:
- Congruence, Triangles
1 (Dolce & Pompeu-adapted) Check the options that are true.
2-In the figure below, the triangles ABC and CDA are congruent. Calculate the value of x and y.
3- Consider the following mathematical problem
Knowing that the triangle ABC below has an isosceles base BC, calculate the value of x.
The solution steps are described in the following items. Explain each one.
The solution steps are described in the following items. Explain each one.a) Note that . Therefore, BP is an angle bisector of .
b) In the triangle BPC, we have =35º and =55º. So =90º.
c) In the triangle CBE, BP is an angle bisector and also the height. So the triangle CBE has an isosceles base on CE. Therefore, P is the midpoint of EC.
d) Now, considering the DEC triangle, where DP is median and height, we conclude that this triangle has an isosceles base EC. So, we have =15º and x=75º.