Question

6. AABC is an isosceles triangle in which 2B 2C and LM || BC. If ZA 50°. 50° (i) Name the type of quadrilateral LMCB (ii) The measure of 2LMC is: (iii) If LALM= = LABC then LM | BC, name the property used. (iv) The measure of ZALM is​

Answer 1

Given the information provided:

- In triangle AABC, A = 50° and is an isosceles triangle,

- LM || BC, 2B = 2C.

(i) Name the type of quadrilateral LMCB:

LMCB is a parallelogram because LM is parallel to BC.

(ii) The measure of 2LMC:

Since LM || BC, 2LMC = 2C = 50° (as given).

(iii) If LALM = LABC, then LM | BC (property used):

If the alternate angles are equal, then the lines are parallel. Therefore, LM || BC is a property of alternate angles.

(iv) The measure of ZALM:

In triangle AALM, as A = 50° and it is an isosceles triangle, so AAA is 180°. Since ALM = MLA, then ZALM = (180 - 50) / 2 = 65°.

Therefore, the measure of ZALM is 65°.