Theorems: Medians in a Triangle

Theorems: Medians in a Triangle. Practice questions to deepen understanding of the theorems on medians in a triangle. Online math practice with full solutions and step-by-step explanations.

Medians in a triangle practice — intersection point of the medians, the 2:1 ratio property. Properties of the median and applications in computations and proofs.

1. The three medians of a triangle meet at a single point. 2. The intersection point divides each median in a 2:1 ratio (the longer segment is closer to the vertex).

15 questions

Question 1
6.67 pts

📐 definition - median:
median segment connecting:
_____ _____ side .

Explanation:

💡 explanation :

1: median 🔍

median ✨
segment connecting vertex

midpoint side
Question 2
6.67 pts

🎯 theorem medians:
three medians :
because _____ one.

Explanation:

💡 explanation :

1: theorem medians 🔍

theorem medians ✨
three medians
because one

Question 3
6.67 pts

📚 terminology:
intersection point three medians :

Explanation:

💡 explanation :

1: 🔍

centroid ✨
intersection point medians

:

2: "centroid"? 📐

Question 4
6.67 pts

🎯 theorem median:
centroid median :

Explanation:

💡 explanation :

1: theorem median 🔍

2:1 ✨
centroid G median
-2

vertex
Question 5
6.67 pts

🎯 Application:
The median AM is 15 cm long.
G is the centroid.
What is the length of AG?

Explanation:

💡 Detailed explanation:

The centroid divides each median in a ratio of 2:1, measured from the vertex.

Therefore the segment from the vertex to the centroid is ⅔ of the full median.

AG = ⅔ · 15 = 10 cm.

Question 6
6.67 pts

🎯 Application:
The length of a median is 18 cm.
G is the centroid.
What is the length of the segment from G to the midpoint of the side?

Explanation:

💡 Detailed explanation:

The centroid divides a median in a ratio of 2:1.

The shorter part, from the centroid to the midpoint of the side, is ⅓ of the whole median.

⅓ · 18 = 6 cm.

Question 7
6.67 pts

🎯 Reverse calculation:
The distance from G, the centroid, to the midpoint of the side is 4 cm.
What is the length of the full median?

Explanation:

💡 Detailed explanation:

The part from the centroid to the midpoint of the side is the shorter part of the median, and it equals ⅓ of the full median.

If ⅓ of the median is 4 cm, then the full median is 4 × 3 = 12 cm.

Question 8
6.67 pts

🎯 isosceles triangle:
median base centroid?

Explanation:

💡 explanation :

1: theorem 🔍

✨
,
3 medians
centroid

No !

2: isosceles triangle 📐

Question 9
6.67 pts

📖 Word problem:
A triangle is made of wire.
The median from vertex A to side BC is 24 cm.
What distance must you travel along the median from vertex A to reach the centroid?

Explanation:

💡 Detailed explanation:

The centroid divides each median in a 2:1 ratio from the vertex.

The distance from the vertex to the centroid is the longer part, equal to ⅔ of the median.

⅔ · 24 = 16 cm.

Question 10
6.67 pts

❓ :
Correct centroid?

Explanation:

💡 explanation :

1: centroid 🔍

✨
centroid
is located always
inside

2:

Question 11
6.67 pts

🏆 Challenge:
In triangle ABC, G is the centroid.
The distance from G to the midpoint of side BC is 5 cm.
What is the distance from vertex A to centroid G?

Explanation:

💡 Detailed explanation:

The centroid divides a median in a 2:1 ratio.

If the shorter part from G to the midpoint is 5 cm, then the longer part from the vertex to G is twice as long.

AG = 2 · 5 = 10 cm.

Question 12
6.67 pts

❓ :
medians ?

Explanation:

💡 explanation :

1: medians 🔍

3 medians ✨

3 medians

median one vertex

Question 13
6.67 pts

🎯 application :
No ,
?

Explanation:

💡 explanation :

1: centroid? 🔍

centroid ✨




2: 📊

Question 14
6.67 pts

📚 summary:
?

Explanation:

💡 explanation :

1: summary theorem 🔍

two theorem ✨
1️⃣ three medians
because one (G)

2️⃣ ce
Question 15
6.67 pts

🎉 :
medians centroid!
because ?

Explanation:

🎊 summary !

1: ? 🔍

🎓 ! 🎓
15
medians centroid

!

2: theorem 📐

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