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Concurrency of Medians of a Triangle

In Δ LMN, ......

Question

In ∆ LMN, .......... is an altitude and .......... is a median. (write the names of appropriate segments.)

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Solution

In ∆ LMN, $segment LX$ is an altitude and $segment LY$ is a median.

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Q. (1) Fill in the blanks.
(i) The perpendicular bisectors of the sides of a triangle are ...... .
(ii) If G is the point of concurrence of the medians of ∆PQR, then the line RG bisects ....... .

(2) In ∆PSI, m∠S = 90° and ST ⊥ PI. Draw ∆PSI and name its altitudes.

(3) Name the medians in the given figure.

Q. Are the median and altitude the same line segments for an equilateral triangle?

Q. Draw a rough figure to illustrate the following statements:

(1) In ∆PQR, seg QN is an altitude.
(2) In ∆NPK, seg PS is a median.
(3) In ∆BCD, seg CM is a median and CE is an altitude.

D E F

is an isosceles triangle and

D G

is the altitude on

F E

D G

Q. If l, m, n are the sides of

Δ

∣ ∣ ∣ ∣ ∣ \begin{matrix} l^{2} & m^{2} & n^{2} (l + 1^{2}) & {(m + 1)}^{2} & {(n + 1)}^{2} {(l - 1)}^{2} & {(m - 1)}^{2} & {(n - 1)}^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

Δ

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Concurrency of Medians of a Triangle

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