Question

1. a rectangle made of square tiles measures 7 tiles long a

wide. what is the length of a similar rectangle whose w
(explore activity)
explain whether the shapes are similar. (examples 1 and
2.
3.
essential question check - in

Explanation:

Step1: Check the angle - equality

For similar triangles, corresponding angles must be equal.
In \(\triangle JKL\), angles are \(40^{\circ},70^{\circ},70^{\circ}\). In \(\triangle PQR\), angles are \(34^{\circ},73^{\circ},73^{\circ}\).
Since \(40^{\circ}
eq34^{\circ}\) and \(70^{\circ}
eq73^{\circ}\), the corresponding angles are not equal.

Step2: Check the side - ratio (though angle - check is sufficient here)

The ratio of the first pair of sides: \(\frac{18}{48}=\frac{3}{8}\). The ratio of the second pair of sides: \(\frac{12}{28}=\frac{3}{7}\).
Since \(\frac{3}{8}
eq\frac{3}{7}\), even if we assume some correspondence (which is wrong as angles don't match), the side - ratios are not equal.

Answer:

The two triangles are not similar. Because for similar triangles, corresponding angles must be equal. In \(\triangle JKL\) the angles are \(40^{\circ},70^{\circ},70^{\circ}\) and in \(\triangle PQR\) the angles are \(34^{\circ},73^{\circ},73^{\circ}\), so the corresponding angles are not equal. Also, if we consider side - ratios (though angle - check is conclusive), \(\frac{18}{48}
eq\frac{12}{28}\) (if we assume some side - correspondence which is wrong as angles don't match).