Question

ACTIVITY 4. THINK THINK THINK! Given are congruent triangles, find the uknown values.

Answer 1

d) SZ = 5cm

e) f)

Explanations:

According to the given diagram, triangle QSZ is similar to the triangle NKH. This shows that:

`\begin{gathered} SZ=KH \\ NK=QS \\ KH=SZ \\ \end{gathered}`

Similarly for the angles:

`\begin{gathered} m\angle N=m\angle Q \\ m\angle K=m\angle S \\ m\angle H=m\angle Z \end{gathered}`

d) Since SZ = KH and the measure of KH is 6cm, hence the measure of SZ will also be 5cm i.e SZ = 5cm

e) Similarly for the angles, we know that measure of angle K will be 87 degrees based on the similarity theorem.

f) To get the measure of the vertex angle Q, we know that the sum of an interior angle of a triangle is 180 degrees, hence;

`\begin{gathered} m\angle Q+m\angle S+m\angle Z=180^0 \\ m\angle Q+87^0+68^0=180^0 \\ m\angle Q+155=180 \\ m\angle Q=180-155 \\ m\angle Q=25^0 \end{gathered}`