Similarity and Dilations: math test, Grade 10 – download the PDF

1 Dilation of a triangle / 3 pts

Triangle \(ABC\) has \(A(4,6)\), \(B(-2,8)\), \(C(10,-6)\). Dilate it from the origin with scale factor \(1.5\). Give \(A'\), \(B'\) and \(C'\).

2 Are they similar? / 4 pts

Triangle \(PQR\) has \(PQ=8\), \(QR=12\), \(PR=14\). Triangle \(STU\) has \(ST=12\), \(TU=18\), \(SU=21\).

1. Show that \(\triangle PQR\sim\triangle STU\).
2. Find the perimeter of \(STU\) using the perimeter ratio.

3 Parallel segment in a triangle / 4 pts

In triangle \(ABC\), \(D\) is on \(AB\) and \(E\) is on \(AC\) with \(DE\parallel BC\). Given \(AD=9\), \(DB=6\), \(DE=12\) and \(EC=4\).

1. Find \(BC\).
2. Find \(AE\).

4 Angle bisector / 3 pts

In triangle \(ABC\), \(AB=14\), \(AC=21\) and \(BC=20\). The bisector of \(\angle A\) meets \(BC\) at \(D\).

1. Write the ratio \(\dfrac{BD}{DC}\).
2. Find \(BD\) and \(DC\).

5 Triangular lots / 3 pts

Two triangular lots are similar. Corresponding sides measure 30 ft and 45 ft. The smaller lot has area 600 ft² and perimeter 100 ft.

1. Find the scale factor from the small to the large lot.
2. Find the area of the larger lot.
3. Find the perimeter of the larger lot.

6 A bow-tie proof / 3 pts

Segments \(AB\) and \(CD\) cross at \(E\) and \(AC\parallel BD\). Also \(EA=10\), \(EB=15\) and \(EC=8\).

1. Prove that \(\triangle EAC\sim\triangle EBD\).
2. Find \(ED\).