Statement 1: In the given figure, P is mid-point of side BC, then AP is a median of triangle ABC.
Statement 2: Every triangle has three sides so three medians. For this reason, BQ and CR are also medians of △ABC.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
A median of a triangle is the line joining a vertex to the mid-point of the opposite side. Since P is the mid-point of BC, AP joins vertex A to the mid-point of the opposite side, so AP is a median. Thus, statement 1 is true.
Every triangle has three vertices and three sides, so it has three medians. As Q and R are the mid-points of AC and AB respectively, BQ and CR are also medians of △ABC. Thus, statement 2 is true.
Hence, option 1 is the correct option.
Statement 1: In the given figure, AP is altitude corresponding to side BC and CR is altitude corresponding to side AB then BQ is altitude corresponding to side AC.
Statement 2: Altitudes of a triangle intersect each other at the same point.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
From the right-angle marks in the figure,
AP ⊥ BC, CR ⊥ AB and BQ ⊥ AC.
Therefore, AP, CR and BQ are the three altitudes of △ABC. Thus, statement 1 is true.
The three altitudes of a triangle are concurrent, i.e. they pass through the same point. Thus, statement 2 is true.
Hence, option 1 is the correct option.