What are Components of a Triangle? [pptime time="0:01"](0:01) [/pptime]

A triangle is a three-sided polygon consisting of three vertices, sides, and angles. Vertices (A, B, C): These are the corner points of the triangle. Sides (a, b, c): These are the edges of the triangle. Side a is opposite vertex A Side b is opposite vertex B Side c is opposite vertex C Angles (α, β, γ): These are the interior angles at each vertex. α is at vertex A β is at vertex B γ is at vertex C Understanding these components is essential for constructing triangles accurately.

How to Construct a Triangle Using ASA? [pptime time="0:37"](0:37) [/pptime]

If you know two angles and the included side , you can construct a unique triangle based on the ASA (Angle-Side-Angle) rule. Draw the given side. Start by drawing side AB = 6 cm as the base of the triangle. Construct the first angle. At point A, use a protractor to measure and draw angle 60°. Construct the second angle. At point B, use a protractor to draw angle 70°. Complete the triangle. Extend both angle lines until they meet at point C.

How to Construct a Triangle Using SAS? [pptime time="1:33"](1:33) [/pptime]

If you know two sides and the included angle , you can construct a unique triangle based on the SAS (Side-Angle-Side) rule. Draw the given side. Start by drawing side AB = 6 cm as the base of the triangle. Construct the given angle. At point B, use a protractor to measure and draw angle 50°. Draw the second side. From point B, extend a line and mark point C such that BC = 5 cm. Complete the triangle. Connect point C to point A to form triangle ABC.

Constructing Triangles with SSA (Ambiguous Case) [pptime time="2:10"](2:10) [/pptime]

If you know two sides and a non-included angle , you may form two different triangles . This is known as the Ambiguous Case in SSA (Side-Side-Angle) triangle construction. Draw the given side. Start by drawing side AB = 7 cm as the base of the triangle. Construct the given angle. At point B, use a protractor to measure and draw angle 40°. Use a compass for the second side. Place the compass at point B and set it to 5 cm. Draw an arc that intersects the extended line from angle B. Identify possible triangles. The arc may intersect the line at two p oints, creating two possible triangles.

How to Construct a Triangle with SSS? [pptime time="3:03"](3:03) [/pptime]

If you know all three sides of a triangle, you can construct a unique triangle using the SSS (Side-Side-Side) rule. Draw the base. Start by drawing side AB = 6 cm as the base of the triangle. Use a compass for the other two sides. Place the compass at point A and set it to 5 cm. Draw an arc. Place the compass at point B and set it to 4 cm. Draw another arc. Find the intersection. The two arcs will intersect at a point. Label this point as C. Complete the triangle. Connect points A to C and B to C to form triangle ABC.

Constructing Triangles - Components, Methods, Examples

🎬 Video: Constructing Triangles Step-by-Step

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What are Components of a Triangle? (0:01)

A triangle is a three-sided polygon consisting of three vertices, sides, and angles.

Vertices (A, B, C): These are the corner points of the triangle.
Sides (a, b, c): These are the edges of the triangle.
- Side a is opposite vertex A
- Side b is opposite vertex B
- Side c is opposite vertex C
Angles (α, β, γ): These are the interior angles at each vertex.
- α is at vertex A
- β is at vertex B
- γ is at vertex C

Understanding these components is essential for constructing triangles accurately.

How to Construct a Triangle Using ASA? (0:37)

If you know two angles and the included side, you can construct a unique triangle based on the ASA (Angle-Side-Angle) rule.

Draw the given side.
Start by drawing side AB = 6 cm as the base of the triangle.
Construct the first angle.
At point A, use a protractor to measure and draw angle 60°.
Construct the second angle.
At point B, use a protractor to draw angle 70°.
Complete the triangle.
Extend both angle lines until they meet at point C.

How to Construct a Triangle Using SAS? (1:33)

If you know two sides and the included angle, you can construct a unique triangle based on the SAS (Side-Angle-Side) rule.

Draw the given side.
Start by drawing side AB = 6 cm as the base of the triangle.
Construct the given angle.
At point B, use a protractor to measure and draw angle 50°.
Draw the second side.
From point B, extend a line and mark point C such that BC = 5 cm.
Complete the triangle.
Connect point C to point A to form triangle ABC.

Constructing Triangles with SSA (Ambiguous Case) (2:10)

If you know two sides and a non-included angle, you may form two different triangles. This is known as the Ambiguous Case in SSA (Side-Side-Angle) triangle construction.

Draw the given side.
Start by drawing side AB = 7 cm as the base of the triangle.
Construct the given angle.
At point B, use a protractor to measure and draw angle 40°.
Use a compass for the second side.
Place the compass at point B and set it to 5 cm. Draw an arc that intersects the extended line from angle B.
Identify possible triangles.
The arc may intersect the line at two points, creating two possible triangles.

How to Construct a Triangle with SSS? (3:03)

If you know all three sides of a triangle, you can construct a unique triangle using the SSS (Side-Side-Side) rule.

Draw the base.
Start by drawing side AB = 6 cm as the base of the triangle.
Use a compass for the other two sides.
- Place the compass at point A and set it to 5 cm. Draw an arc.
- Place the compass at point B and set it to 4 cm. Draw another arc.
Find the intersection.
The two arcs will intersect at a point. Label this point as C.
Complete the triangle.
Connect points A to C and B to C to form triangle ABC.