Question

11/7 - isosceles and equilateral practice
possible points: 1.6
given: ab=cb=cd. p = 21
(figure not drawn to scale.)
q=
r=
s=
t=

Explanation:

Step1: Find \( q \)

Since \( AB = CB \), in \(\triangle ABC\), \( q=p \) (isosceles triangle property: angles opposite equal sides are equal). Given \( p = 21\), so \( q = 21\).

Step2: Find \( r \)

In \(\triangle ABC\), using the exterior - angle theorem. The exterior angle \( r\) of \(\triangle ABC\) is \(r=p + q\). Substituting \(p = 21\) and \(q = 21\), we get \(r=21+21=42\).

Step3: Find \( s \)

Since \( CB = CD \), in \(\triangle BCD\), \(s = r\) (isosceles triangle property: angles opposite equal sides are equal). So \(s = 42\).

Step4: Find \( t \)

In \(\triangle ACD\), using the exterior - angle theorem. \(t=p + s\). Substituting \(p = 21\) and \(s = 42\), we get \(t=21 + 42=63\).

Answer:

\(q = 21\), \(r = 42\), \(s = 42\), \(t = 63\)