Question

question
determine if triangle bcd and triangle efg are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Find angle C in triangle BCD

The sum of angles in a triangle is \(180^\circ\). In \(\triangle BCD\), we know \(\angle B = 46^\circ\) and \(\angle D = 63^\circ\). So, \(\angle C=180^\circ - 46^\circ - 63^\circ\)
\(\angle C = 71^\circ\)

Step2: Find angle E in triangle EFG

In \(\triangle EFG\), \(\angle G = 63^\circ\) and \(\angle F = 72^\circ\). So, \(\angle E=180^\circ - 63^\circ - 72^\circ\)
\(\angle E = 45^\circ\)

Step3: Compare angles of the two triangles

For triangles to be similar, their corresponding angles must be equal. In \(\triangle BCD\), angles are \(46^\circ\), \(63^\circ\), \(71^\circ\). In \(\triangle EFG\), angles are \(45^\circ\), \(63^\circ\), \(72^\circ\). Since the angles do not match ( \(46^\circ
eq45^\circ\) and \(71^\circ
eq72^\circ\) ), the triangles are not similar.

Answer:

Triangle \(BCD\) and triangle \(EFG\) are not similar because their corresponding angles are not equal (angles in \(\triangle BCD\) are \(46^\circ\), \(63^\circ\), \(71^\circ\) and in \(\triangle EFG\) are \(45^\circ\), \(63^\circ\), \(72^\circ\)).