In triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC. If AC = 9 cm, then what is CF equal to?
2.25 cm
Concept:
Median: A line segment that joins a vertex to the mid-point of the
the side that is opposite to that vertex
Basic proportionality theorem(BPT): If a line is drawn parallel to
one side of a triangle intersecting the other two sides in distinct
points, then the other two sides are divided in the same ratio.
Calculation:
Given that,
AD and BE are medians of BC and AC respectively.
⇒ BC = 2DC ------(1)
Also, we have AC = 9 cm
⇒ AE = EC = 9/2 = 4.5
In triangle CBE, DF ∥ BE
Using the Basic proportionality theorem
⇒ \(\frac{DC}{BC} = \frac{FC}{EC}\)
⇒ \(\frac{DC}{2DC} = \frac{FC}{4.5}\)
⇒ FC = 4.5/2 = 2.25 cm
∴ CF = 2.25 cm.
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Important Questions from Triangles, Congruence and Similarity
In a $\Delta ABC$, $\angle C = (9/4) \angle B = (3/2) (\angle A+\angle B)$. Find the measure of the angles.
- The areas of two similar triangles $\Delta$XYZ and $\Delta$LMN are 49 cm$^2$ and 9 cm$^2$, respectively. If LM = 9 cm, then the length of XY is:
Triangles \(PQR\) and \(ABC\) are similar triangles. Triangle \(ABC\) have the following sides
\(AB = 12 \text{ cm}\),
\(AC = 15 \text{ cm}\),
\(CB = 21 \text{ cm}\).
Triangle \(PQR\) have the following sides:
\(PQ = 4 \text{ cm}\),
\(RQ = 7 \text{ cm}\).
What is the length of side \(PR\)?
For a pair of similar triangles, the angles made at \(Q\) is same in both the triangles \(PQR\) and \(LQJ\).
If the length of side \(QJ\) is 10 cm and \(QR\) is 5 cm, what is the ratio of their total areas?- In $\Delta ABC$ $\overline{PQ} \parallel \overline{AB}$. P and Q are on BC and CA respectively. If CQ : QA = 1 : 3 and CP = 4, then what is the value of BC?
