Podcast
Questions and Answers
In triangle $\triangle ABC$, if $AB = 12cm$, $BC = 8cm$, and $AC = 15cm$, what information is provided?
In triangle $\triangle ABC$, if $AB = 12cm$, $BC = 8cm$, and $AC = 15cm$, what information is provided?
- The measure of all angles
- The length of all three sides (correct)
- The area of the triangle
- The height of the triangle
If $\triangle ABC$ and $\triangle PQR$ are similar and $AB = 12cm$ and $PQ = 18cm$, what does this indicate about the relationship between the triangles?
If $\triangle ABC$ and $\triangle PQR$ are similar and $AB = 12cm$ and $PQ = 18cm$, what does this indicate about the relationship between the triangles?
- $\triangle PQR$ is congruent to $\triangle ABC$
- The triangles have different shapes
- $\triangle PQR$ is larger than $\triangle ABC$ (correct)
- $\triangle PQR$ is smaller than $\triangle ABC$
In $\triangle ABC$, a line $DE$ is parallel to $BC$. What does this imply about the relationship between $\triangle ADE$ and $\triangle ABC$?
In $\triangle ABC$, a line $DE$ is parallel to $BC$. What does this imply about the relationship between $\triangle ADE$ and $\triangle ABC$?
- They have different angle measures.
- They are congruent.
- They have the same area.
- They are similar. (correct)
If $DE$ is parallel to $BC$ in $\triangle ABC$, and $AB = 8cm$ and $DB = 5cm$, what is the length of $AD$?
If $DE$ is parallel to $BC$ in $\triangle ABC$, and $AB = 8cm$ and $DB = 5cm$, what is the length of $AD$?
In $\triangle ABC$, with $DE \parallel BC$, if $AE = 2x + 4$ and $EC = 3x - 5$, what needs to be known to find the exact lengths of $AE$ and $EC$?
In $\triangle ABC$, with $DE \parallel BC$, if $AE = 2x + 4$ and $EC = 3x - 5$, what needs to be known to find the exact lengths of $AE$ and $EC$?
Flashcards
Similar Triangles
Similar Triangles
Triangles with the same shape but potentially different sizes. Their corresponding angles are equal, and corresponding sides are in proportion.
Triangle Proportionality Theorem
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.
Finding Side Lengths in Similar Triangles
Finding Side Lengths in Similar Triangles
To find the length of the sides of a similar triangle, set up a proportion using corresponding sides.
Corresponding Angles in Similar Triangles
Corresponding Angles in Similar Triangles
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Right Triangle
Right Triangle
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Study Notes
- Two example problems are given
- The first one is about two similar triangles ABC and PQR
Problem 4.2.1
- Triangle ABC and triangle PQR are similar
- AB = 12cm
- BC = 8cm
- AC = 15 cm
- PQ = 18 cm
- Find the length of the other sides of triangle PQR
- Find all the angles in triangle ABC and triangle PQR
Problem 4.2.2
- In triangle ABC, segment DE is parallel to BC, with D on AB
- AB = 8 cm
- DB = 5 cm
- AE = 2x + 4 cm
- EC = 3x - 5 cm
- Angle B = 90 degrees
- Find the length of BC
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Description
Solve problems using properties of similar triangles. Find unknown side lengths and angles in triangles ABC and PQR. Also, determine the length of BC given parallel segments within triangle ABC.
