Consider each option one at a time. Use Theorem 5.10.
B
Practice makes perfect
To find the false statement, let's consider each option one at a time.
Option A
It is given that DC is a median of â–³ ABC. By the definition, a median connects a triangle's vertex with the midpoint of the opposite side. In our case C is a vertex, so D must be the midpoint of AB. Therefore, segments AD and BD have the same measure.
The statement is true.
Option B
We know that ∠1 has a greater measure than ∠2. Using the points on the diagram, we can name ∠1 as ∠ADC and ∠2 as ∠BDC. Thus, the following inequality is true.
m∠ADC > m∠BDC
We can conclude that the statement is false.
Option C
To verify whether this statement is true, let's use Theorem 5.10.
If one angle of a triangle has
a greater measure than another angle,
then the side opposite to the greater angle
is longer than the side opposite
to the lesser angle.
Now, we need to consider this theorem in relation to â–³ ABC.
We are told that m∠1 is greater than m∠2. From the diagram, we can see that AC is opposite to ∠1 and BC is opposite to 2. Therefore, by the above theorem, side AC is longer than BC.
AC>BC
The statement is true.
Option D
Unfortunately, there is not enough information to prove that m∠1 is greater than m∠B. However, we have already found that option B is not true. Therefore, the answer is B.
