Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
In triangle ABC, if $DE$ is parallel to $BC$, which statement is true?
In triangle ABC, if $DE$ is parallel to $BC$, which statement is true?
- $\frac{AD}{AE} = \frac{DB}{EC}$
- $\frac{AD}{DB} = \frac{AB}{AC}$
- $\frac{AD}{AC} = \frac{DB}{BE}$
- $\frac{AD}{DB} = \frac{AE}{EC}$ (correct)
What can be concluded if $\frac{AD}{DB} = \frac{AE}{EC}$ in triangle $ABC$?
What can be concluded if $\frac{AD}{DB} = \frac{AE}{EC}$ in triangle $ABC$?
- $BD$ bisects $\angle BAC$
- $AD$ is parallel to $EC$
- $AE$ is parallel to $BC$
- $DE$ is parallel to $BC$ (correct)
In triangle $ABC$, $AD$ is the bisector of $\angle BAC$. Which of the following is true?
In triangle $ABC$, $AD$ is the bisector of $\angle BAC$. Which of the following is true?
- $\frac{BD}{DC} = \frac{AB}{AC}$ (correct)
- $\frac{BD}{BC} = \frac{AC}{AB}$
- $\frac{BA}{BD} = \frac{CA}{AD}$
- $\frac{BD}{AB} = \frac{AC}{DC}$
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?
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?
Signup and view all the answers
Which statement is the converse of the basic proportionality theorem?
Which statement is the converse of the basic proportionality theorem?
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of fundamental geometry theorems and properties, including the Basic Proportionality Theorem, Converse of Basic Proportionality Theorem, and more.
