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In this lesson, we will learn how to identify and use medians and altitudes of triangles.

Q1:

In β³ π π π , where π΄ is the midpoint of π π , what name is given to π΄ π ?

Q2:

In a triangle π΄ π΅ πΆ , π is the point of concurrency of its medians. If π΄ π· is a median, then π΄ π = π π· .

Q3:

What is length π π΅ rounded to the nearest hundredth?

Q4:

Find the length π΄ π , given that π΄ πΈ = 5 4 .

Q5:

Determine the lengths of π΅ π· and π΄ π΅ .

Q6:

In β³ π½ πΎ πΏ , π π = 2 . 1 c m . Find the length of π πΏ .

Q7:

In β³ πΎ π π» , πΎ π = 2 and π π = ( 5 π₯ β 7 ) . Find π₯ .

Q8:

In the given figure, segments π΄ π· and πΆ πΈ are the medians of β³ π΄ πΆ π΅ , where π΄ π· β πΆ πΈ , π΄ π΅ = 1 7 . 7 c m , and πΆ πΈ = 9 c m . Determine πΆ π΄ to the nearest tenth.

Q9:

In β³ π½ πΎ πΏ , π½ π = 6 c m . Find the length of π π .

Q10:

Given that the area of β³ π΄ πΈ πΆ = 2 5 5 c m ο¨ , find the area of β³ π΄ π΅ πΆ .

Q11:

Find the length of π΅ π· and the perimeter of β³ π΄ π΅ π· .

Q12:

Equilateral triangle π΄ π΅ πΆ has side 50.6. Given that π is the intersection of its medians, determine ο π π΅ β ο πΆ π .

Q13:

Given that π πΎ is a median of β³ π½ πΏ π , π½ πΎ = 3 π¦ β 8 , and πΏ πΎ = 2 π¦ β 4 , find the length of πΏ πΎ .

Q14:

Use the data in the figure to determine the length of π· πΉ and then the perimeter of β³ π· πΈ πΉ .

Q15:

In triangle π΄ π΅ πΆ , π΄ π΅ = π΄ πΆ = 1 0 c m , π΅ πΆ = 1 2 c m and π· is the midpoint of π΅ πΆ . Find the length of π΄ π· .

Q16:

In triangle π΄ π΅ πΆ , π΄ π΅ = π΄ πΆ = 1 0 c m , π΅ πΆ = 1 6 c m and π· is the midpoint of π΅ πΆ . Find the length of π΄ π· .

Q17:

Given that π΄ π· = 9 c m and πΈ π΅ = π΄ π΅ , find the perimeter of β³ π π· πΈ .

Q18:

Given that π΄ π΅ = π΄ πΆ = 2 2 c m , πΆ π΅ = 2 0 c m , and πΈ π΅ = πΈ πΆ , find the length of π΄ π· .

Q19:

What is the length of πΆ π· ?

Q20:

Given that point πΈ bisects π΅ πΆ , point π· bisects π΄ π΅ , π΄ πΈ and πΆ π· intersect at point π , and π΄ πΈ = 3 3 c m , find the length of π πΈ .

Q21:

Given that π is the point of intersection of the medians, π΄ π· = 4 . 3 6 c m , π΅ π = 3 . 4 7 c m , and π πΉ = 1 . 5 9 c m , find the lengths of π΄ π , π πΈ , and πΆ πΉ to the nearest hundredth.

Q22:

In the figure, calculate the length of π΄ π· .

Q23:

Given that πΈ π = 1 4 3 c m and π΄ π = 2 π π· , find the length of π· πΉ .

Q24:

Given that πΈ π· = 7 . 5 c m , find the lengths of π΄ πΆ and π΅ πΈ .

Q25:

Given that π΄ π΅ πΆ π· is a parallelogram, which line segment is a median in β³ π΄ π΅ π· ?

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