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Medians and Centroid of a Triangle

Geometry and Measures Medians and Centroid of a Triangle

🎬 Video:

📂 Flashcards:

The definition of a median of a triangle is that it connects a vertex to the midpoint of the opposite side, dividing it into two equal-area triangles. — 1) Median of a Triangle

The definition of the centroid of a triangle is the point where the three medians intersect, dividing each median in a 2:1 ratio. — 2) Centroid of a Triangle

The median and centroid of a triangle apply to the problem. — 3) Practice - Median and Centroid of a Triangle

🍪 Quiz:

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Medians and Centroid of a Triangle

1 / 6

Q: AD is a median of triangle ABC. If BD = 5 cm, what is the length of CD?

$Triangle ABC with median AD, point D on base BC dividing it into 5?cm and unknown length marked with a question mark.$

5 cm

6 cm

10 cm

4 cm

Feedback: Not quite! A median connects a vertex to the midpoint of the opposite side, so BD = CD.

Feedback: Well done! A median connects a vertex to the midpoint of the opposite side, so BD = CD.

2 / 6

Q: What is the name of the point where the medians of a triangle intersect?

Circumcentre

Centroid

Incentre

Orthocentre

Feedback: Not quite! The centroid is where all three medians of a triangle meet. It always lies inside the triangle, no matter the triangle’s shape.

Feedback: Well done! The centroid is where all three medians of a triangle meet. It always lies inside the triangle, no matter the triangle’s shape.

3 / 6

Q: If AD is a median and E is the centroid of triangle ABC, and AE = 6 cm, what is the length of ED?

$Triangle ABC with median AD, point E on AD marked 6 cm from A, unknown distance from D to E shown with a question mark.$

3 cm

4 cm

2 cm

6 cm

Feedback: Not quite! The centroid divides the median in a 2:1 ratio. Since AE is the longer segment, ED is half of AE, so ED = 6 cm ÷ 2 = 3 cm.

Feedback: Well done! The centroid divides the median in a 2:1 ratio. Since AE is the longer segment, ED is half of AE, so ED = 6 cm ÷ 2 = 3 cm.

4 / 6

Q: If CG is a median and E is the centroid of triangle ABC, and the area of triangle AGC is 10 cm², what is the area of triangle ABC?

$Triangle ABC with shaded triangle AGC, area 10 cm², and point E marked on median GC.$

20 cm²

6 cm²

12 cm²

8 cm²

Feedback: Not quite! The centroid divides the median in a 2:1 ratio. The longer segment (BE) is two-thirds of the total length (BF): $BE = \frac{2}{3} \times 12 = 8 \text{ cm}$.

Feedback: Well done! The centroid divides the median in a 2:1 ratio. The longer segment (BE) is two-thirds of the total length (BF): $BE = \frac{2}{3} \times 12 = 8 \text{ cm}$.

5 / 6

Q: If BF is a median and E is the centroid of triangle ABC, and BF = 12 cm, what is the length of BE?

$Triangle ABC with median BF, point E on BF and BF = 12 cm, unknown length from E to F shown with a question mark.$

3 cm

8 cm

6 cm

4 cm

Feedback: Not quite! The centroid divides the median in a 2:1 ratio. The longer segment (BE) is two-thirds of the total length (BF): $BE = \frac{2}{3} \times 12 = 8 \text{ cm}$.

Feedback: Well done! The centroid divides the median in a 2:1 ratio. The longer segment (BE) is two-thirds of the total length (BF): $BE = \frac{2}{3} \times 12 = 8 \text{ cm}$.

6 / 6

Q: If E is the centroid of triangle ABC, and you know that AE= 10 cm, what is the length of the median AD?

$Triangle ABC with medians intersecting at E, AE marked 10 cm with unknown length from E to midpoint of BC shown in pink.$

16 cm

13 cm

12 cm

15 cm

Feedback: Not quite! The centroid divides the median in a 2:1 ratio. ED, as the shorter segment, is half of AE, which is 5 cm. So AD = AE + ED = 10 + 5 = 15 cm.

Feedback: Well done! The centroid divides the median in a 2:1 ratio. ED, as the shorter segment, is half of AE, which is 5 cm. So AD = AE + ED = 10 + 5 = 15 cm.

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