Show the similarity between a triangle with angles A, B, and C, where m∠A=47° and m∠B=36°, and another triangle with angles G, H, and J, where m∠G=36° and m∠J=97°.

Question

Responses

△ABC∼△HJG

△ABC∼△HGJ

△ABC∼△GHJ

△ABC∼△GJH

Answer 1

To determine the similarity between the two triangles, we need to calculate the angles of triangle \( ABC \) and triangle \( GHJ \).

For triangle \( ABC \):

• \( m\angle A = 47^\circ \)
• \( m\angle B = 36^\circ \)

To find \( m\angle C \): \[ m\angle C = 180^\circ - (m\angle A + m\angle B) = 180^\circ - (47^\circ + 36^\circ) = 180^\circ - 83^\circ = 97^\circ \]

So, the angles of triangle \( ABC \) are:

• \( m\angle A = 47^\circ \)
• \( m\angle B = 36^\circ \)
• \( m\angle C = 97^\circ \)

Now for triangle \( GHJ \):

• \( m\angle G = 36^\circ \)
• \( m\angle J = 97^\circ \)

To find \( m\angle H \): \[ m\angle H = 180^\circ - (m\angle G + m\angle J) = 180^\circ - (36^\circ + 97^\circ) = 180^\circ - 133^\circ = 47^\circ \]

So, the angles of triangle \( GHJ \) are:

• \( m\angle G = 36^\circ \)
• \( m\angle H = 47^\circ \)
• \( m\angle J = 97^\circ \)

Now we can list the angles of both triangles:

• Triangle \( ABC \): \( 47^\circ, 36^\circ, 97^\circ \)
• Triangle \( GHJ \): \( 36^\circ, 47^\circ, 97^\circ \)

Since the angles of both triangles are the same, we can conclude that: \[ \triangle ABC \sim \triangle GHJ \]

Thus, the answer is: \(\triangle ABC \sim \triangle GHJ\)