Question

ex 21 given astw ≅ △bfn, find each missing measure.
a) bn =
b) tw =
c) bf =
d) m∠w =
e) m∠b =
f) m∠f =

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle STW\cong\triangle BFN\), corresponding sides and angles are equal.

• For side \(BN\): \(BN = SW = 9\mathrm{cm}\) (corresponding sides of congruent triangles)
• For side \(TW\): \(TW=FN = 14\mathrm{cm}\) (corresponding sides of congruent triangles)
• For side \(BF\): \(BF = ST=17\mathrm{cm}\) (corresponding sides of congruent triangles)
• For angle \(m\angle W\): \(m\angle W=m\angle N = 82^{\circ}\) (corresponding angles of congruent triangles)
• For angle \(m\angle B\): \(m\angle B=m\angle S = 67^{\circ}\) (corresponding angles of congruent triangles)
• For angle \(m\angle F\): In a triangle, the sum of interior angles is \(180^{\circ}\). In \(\triangle BFN\), \(m\angle F=180^{\circ}-m\angle B - m\angle N\). Substitute \(m\angle B = 67^{\circ}\) and \(m\angle N=82^{\circ}\), we get \(m\angle F=180^{\circ}-67^{\circ}-82^{\circ}=31^{\circ}\)

Answer:

a) \(BN = 9\mathrm{cm}\)
b) \(TW = 14\mathrm{cm}\)
c) \(BF = 17\mathrm{cm}\)
d) \(m\angle W=82^{\circ}\)
e) \(m\angle B = 67^{\circ}\)
f) \(m\angle F=31^{\circ}\)