A triangle is written of 3 line segments. The line segments crossing in their endpoints. To name a triangle we regularly use the vertices (the surname of the endpoints). The triangle below is named ABC.

You are watching: A triangle with one right angle and no congruent sides

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A triangle has three angles. The sum of the steps of the angle is constantly 180° in a triangle.

We have actually different varieties of triangles. A triangle is share by its angles and by the variety of congruent sides.

A triangle that has three acute angels is called an acute triangle.

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A triangle that has one right angle is called a ideal triangle.

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A triangle that has one obtuse edge is referred to as an obtuse triangle.

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When a triangle has actually three congruent sides, we call the triangle an equilateral triangle. We mark the congruent political parties by a cut mark. The angles in an it is provided triangle are constantly 60°.

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When a triangle has two congruent sides it is dubbed an isosceles triangle. The angle opposite come the two sides of the same size are congruent.

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A triangle without any kind of congruent political parties or angle is called a scalene triangle.

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When two triangles room congruent it means that they have the exact same size and shape. This means that they have the exact same angles. The red cut marks display us i beg your pardon sides and also angles that space congruent Congruency is shown by this symbol

$$\cong$$

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$$\beginmatrix A\cong X & & AB\cong XY\\ B\cong Y & & BC\cong YZ\\ C\cong Z & & AC\cong XZ \endmatrix$$

Triangles that have congruent angles however not the same size are dubbed similar. Similar triangles have sides that are proportional. Similarity is presented by this symbol

$$\sim$$

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$$\bigtriangleup ABC\sim \bigtriangleup XYZ$$

$$A=X,\: \: B=Y,\: \: C=Z$$

$$\fracax=\fracby=\fraccz$$

Example

Find x in the comparable triangles.

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We recognize that since the triangle are comparable the sides room proportional which way that

$$\fracx14=\frac321\Rightarrow$$

$$x=\frac14\cdot 321=\frac4221=2$$

$$x=2$$

Video lesson

Find the end whether the triangles room right, isosceles, acute, scalene, obtuse or equilateral