Which of the triangle(s) shown is similar to triangle c? b d e f g h

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21-06-2017
Mathematics

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Which of the triangle(s) shown is similar to triangle c? b d e f g h

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calculista calculista · Answer 1 · 2018-12-08T02:11:14+01:00

Answer:

Triangle h

Step-by-step explanation:

we know that

The measure of the internal angles of the right triangle c are

[tex]30\°-90\°-60\°[/tex]

The triangle e is a right triangle but the measure of the internal angles are

[tex]45\°-90\°-45\°[/tex] ------> is not the solution

The triangle f is a right triangle but the measure of the internal angles are

[tex]45\°-90\°-45\°[/tex] ------> is not the solution

The triangle h is a right triangle and the measure of the internal angles are

[tex]30\°-90\°-60\°[/tex] ------> is the solution

AkshayG AkshayG · Answer 2 · 2019-11-30T10:23:41+01:00

The triangle h is similar to triangle c by AA Similarity Theorem.

Further Explanation:

The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.

There are many similarity rules and are as follows.

1. Angle Angle (AA)

2. Side SideSide (SSS)

3. Side Angle Side (SAS)

Explanation:

In triangle (a)

The two angles are [tex]{60^ \circ }{\text{ and }}{60^ \circ }.[/tex]

The third angle can be obtained as follows,

[tex]\begin{aligned}{\text{Angle}}&= {180^ \circ } - {60^ \circ } - {60^ \circ }\\&= {60^ \circ }\\\end{aligned}[/tex]

All the angles are of [tex]{60^ \circ }.[/tex]

Triangle (b) is an isosceles triangle.

The angles of the triangle are [tex]{30^ \circ },{75^ \circ }{\text{ and }}{75^ \circ }.[/tex]

Triangle (c) is a right angles triangle.

The angles are [tex]{30^ \circ },{90^ \circ }{\text{ and }}{60^ \circ }.[/tex]

The angles of triangle (e) are [tex]{45^ \circ },{90^ \circ }{\text{ and }}{45^ \circ }.[/tex]

The angles of triangle (f) are [tex]{45^ \circ },{90^ \circ }{\text{ and }}{45^ \circ }.[/tex]

The angles of triangle (g) are [tex]{45^ \circ },{67.5^ \circ }{\text{ and }}{67.5^ \circ }.[/tex]

Triangle (h) is a right angles triangle.

The angles are [tex]{30^ \circ },{90^ \circ }{\text{ and }}{60^ \circ }.[/tex]

Therefore, triangle (c) and triangle (h) are similar to each other by AA Similarity Theorem.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: similar, two triangles, congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle, similarity theorem, SSS congruency theorem, SSS similarity theorem, AA similarity postulate, SAS congruency postulate.