Podcast
Questions and Answers
What is a Unique Triangle?
What is a Unique Triangle?
The outcome of conditions that would allow you to create only one triangle.
What does it mean to have Many Nonidentical Triangles?
What does it mean to have Many Nonidentical Triangles?
The outcome of conditions that would allow you to create many different triangles that do not look the same.
What does it mean to have Many Similar Triangles?
What does it mean to have Many Similar Triangles?
The outcome of conditions that would allow you to create many triangles with the same shape but in different sizes.
What conditions could lead to No Triangle at all?
What conditions could lead to No Triangle at all?
What are the conditions that lead to Unique Triangles?
What are the conditions that lead to Unique Triangles?
What are the conditions that lead to Nonidentical Triangles?
What are the conditions that lead to Nonidentical Triangles?
What conditions lead to Many Similar Triangles?
What conditions lead to Many Similar Triangles?
What is the sum of the angles in a triangle?
What is the sum of the angles in a triangle?
What is an Isosceles Triangle?
What is an Isosceles Triangle?
What is an Equilateral Triangle?
What is an Equilateral Triangle?
What is a Right Triangle?
What is a Right Triangle?
What is an Acute Triangle?
What is an Acute Triangle?
What is an Obtuse Triangle?
What is an Obtuse Triangle?
Given the side lengths 5mm, 1mm, and 1mm, what kind of triangle can be formed?
Given the side lengths 5mm, 1mm, and 1mm, what kind of triangle can be formed?
Given lengths 5mm, 8mm, and 8mm, how many triangles can be formed?
Given lengths 5mm, 8mm, and 8mm, how many triangles can be formed?
For side lengths 9ft, 1ft, and 6ft, what can be formed?
For side lengths 9ft, 1ft, and 6ft, what can be formed?
For angles 72°, 34°, and 74°, how many similar triangles can be formed?
For angles 72°, 34°, and 74°, how many similar triangles can be formed?
For angle measurements of 100°, 70°, and 40°, what kind of triangle can be formed?
For angle measurements of 100°, 70°, and 40°, what kind of triangle can be formed?
Given angles 90°, 25°, and 85°, what can be formed?
Given angles 90°, 25°, and 85°, what can be formed?
Given side lengths of 3in, 8in and an included angle of 75°, how many unique triangles can be formed?
Given side lengths of 3in, 8in and an included angle of 75°, how many unique triangles can be formed?
Given the angles 27°, 39° and an included side of 17cm, how many unique triangles can be formed?
Given the angles 27°, 39° and an included side of 17cm, how many unique triangles can be formed?
If an Isosceles triangle has a base angle measuring 35°, what are the measures of the other two angles?
If an Isosceles triangle has a base angle measuring 35°, what are the measures of the other two angles?
In a triangle with angles measuring 46° and 103°, what is the measure of the third angle?
In a triangle with angles measuring 46° and 103°, what is the measure of the third angle?
Flashcards
Unique Triangle
Unique Triangle
Formed when conditions allow for only one possible triangle.
Many Nonidentical Triangles
Many Nonidentical Triangles
Conditions allow for multiple different triangles to be created.
Many Similar Triangles
Many Similar Triangles
Conditions create multiple triangles that share the same shape, but differ in size.
No Triangle
No Triangle
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Unique Triangle Conditions
Unique Triangle Conditions
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Nonidentical Triangle Conditions
Nonidentical Triangle Conditions
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Similar Triangle Conditions
Similar Triangle Conditions
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No Triangle Condition (Sides)
No Triangle Condition (Sides)
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No Triangle Condition (Angles)
No Triangle Condition (Angles)
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Sum of Angles in a Triangle
Sum of Angles in a Triangle
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Isosceles Triangle
Isosceles Triangle
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Equilateral Triangle
Equilateral Triangle
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Right Triangle
Right Triangle
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Acute Triangle
Acute Triangle
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Obtuse Triangle
Obtuse Triangle
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Study Notes
Triangle Types and Conditions
- Unique Triangle: Formed when conditions allow for only one triangle to be created.
- Many Nonidentical Triangles: Conditions enable multiple triangles that differ in appearance.
- Many Similar Triangles: Conditions lead to numerous triangles sharing the same shape but differing in size.
- No Triangle at all: When given conditions make it impossible to form a triangle.
Conditions for Triangle Formation
- Unique Triangle Conditions: Combinations of Angle, Side, Angle (ASA), Side, Angle, Side (SAS), or Side, Side, Side (SSS) with the added criterion that a + b > c.
- Nonidentical Triangle Conditions: Often arise when only one or two angles or sides are provided, leading to various configurations.
- Similar Triangle Conditions: Established with Angle, Angle, Angle (AAA) criteria, resulting in triangles of the same shape.
Criteria Leading to No Triangle
- If sides do not meet triangle inequalities, such as a + b = c or a + b < c.
- If angle measures do not sum to 180 degrees, either exceeding or falling short.
Properties of Triangles
- Sum of Angles in a Triangle: Always equals 180 degrees.
- Isosceles Triangle: Contains two congruent sides with equal base angles.
- Equilateral Triangle: All three sides are congruent, with angles measuring 60 degrees each.
- Right Triangle: Features one 90-degree angle and two acute angles.
- Acute Triangle: All angles are acute.
- Obtuse Triangle: Contains one obtuse angle (> 90 degrees) and two acute angles.
Example Problems and Solutions
- Example 1: Sides 5mm, 1mm, and 1mm yield no triangle.
- Example 2: Sides 5mm, 8mm, and 8mm form one unique triangle.
- Example 3: Sides 9ft, 1ft, and 6ft create no triangle.
- Example 4: Angles 72°, 34°, and 74° can lead to many similar triangles.
- Example 5: Angles 100°, 70°, and 40° result in no triangle.
- Example 6: Angles 90°, 25°, and 85° do not form a triangle.
- Example 7: Sides 3 in, 8 in, with an included angle of 75° create one unique triangle.
- Example 8: Angles 27°, 39° with a side of 17 cm yield one unique triangle.
Additional Example
- Isosceles Triangle Problem: With a base angle of 35°, the other two angles measure 35° and 110° respectively.
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