Question

In digram shown below, line abc and triangle abf = triangle bcd. prove: line bf||cd

a) angle abc = angle bcd
b) angle fba = angle dcb
c) angle abf = angle dcb
d) angle fba = angle cdb

Answer 1

a) angle abc = angle bcdb

Step-by-step explanation:

In the given diagram, we have line abc and triangle abf = triangle bcd. To prove that line bf is parallel to cd, we can use the property that corresponding angles of congruent triangles are equal. Therefore, we can conclude that angle abc is equal to angle bcdb, which implies that line bf is parallel to cd.

Firstly, by the property of congruent triangles, we know that angle abc is equal to angle bcd because triangle abf is congruent to triangle bcd. This establishes the equality of these two angles. Secondly, according to the transitive property of equality, if angle abc is equal to angle bcd and angle fba is also equal to angle abc, then it follows that angle fba is equal to angle bcd. This further supports the conclusion that line bf is parallel to cd.

In summary, based on the properties of congruent triangles and the transitive property of equality, we have proven that line bf is parallel to cd by establishing the equality of corresponding angles in congruent triangles.

So correct option is a) angle abc = angle bcdb