5 Questions
In triangle ABC, if $DE$ is parallel to $BC$, which statement is true?
$\frac{AD}{DB} = \frac{AE}{EC}$
What can be concluded if $\frac{AD}{DB} = \frac{AE}{EC}$ in triangle $ABC$?
$DE$ is parallel to $BC$
In triangle $ABC$, $AD$ is the bisector of $\angle BAC$. Which of the following is true?
$\frac{BD}{DC} = \frac{AB}{AC}$
If $AB$, $CD$, and $EF$ are three parallel lines and $l$ and $m$ are two transversals that intersect these lines, which of the following is true?
$\frac{AB}{CD} = \frac{BC}{EF}$
Which statement is the converse of the basic proportionality theorem?
If $\frac{AD}{DB} = \frac{AE}{EC}$ then $DE$ is parallel to $BC$
Study Notes
Proportionality Theorems
- If DE is parallel to BC, then the ratio of AD to DB is equal to the ratio of AE to EC.
- Conversely, if the ratio of AD to DB is equal to the ratio of AE to EC, then DE is parallel to BC.
Angle Bisector Theorem
- If AD is the bisector of angle BAC, then the ratio of BD to DC is equal to the ratio of AB to AC.
Three Parallel Lines and Transversals
- If three lines AB, CD, and EF are parallel, and two transversals l and m intersect them, then the ratio of AB to CD is equal to the ratio of BC to EF.
Test your understanding of fundamental geometry theorems and properties, including the Basic Proportionality Theorem, Converse of Basic Proportionality Theorem, and more.
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