Practice sheet

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Dilate $A(3, 1)$ about the origin with scale factor 2. Tap its image.
A dilation takes a segment of length 3 to a segment of length 11. Find the scale factor.
A triangle is dilated with scale factor 5. What happens to its angles?
1. They stay the same
2. They are multiplied by 5
3. They grow by 5 degrees
A triangle is dilated with scale factor 2. What happens to its angles?
1. They stay the same
2. They are multiplied by 2
3. They grow by 2 degrees
A triangle is dilated with scale factor 4. What happens to its angles?
1. They stay the same
2. They are multiplied by 4
3. They grow by 4 degrees
A triangle is dilated with scale factor 3. What happens to its angles?
1. They stay the same
2. They are multiplied by 3
3. They grow by 3 degrees
Two polygons are similar. A side of length 5 corresponds to a side of length 15. Another side of the small polygon has length 9. Find the matching side of the large one.
A polygon has perimeter 20. It is enlarged by a scale factor of 5. Find the new perimeter.
A shape has area 9. It is enlarged by a scale factor of 2. Find the new area.
Two triangles each have a $76^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $43^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $35^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $69^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $65^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $67^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $73^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $51^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $30^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $32^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $60^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $33^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $39^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $61^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $47^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $70^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $31^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $79^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $46^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $58^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $44^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $57^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $40^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $53^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $45^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $41^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $62^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $34^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $38^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $78^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $66^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $37^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $55^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $48^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $59^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $63^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $71^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $56^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $54^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $52^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $68^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $75^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $72^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $50^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $49^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $74^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $77^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $42^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $80^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
Two triangles each have a $36^\circ$ angle and a $50^\circ$ angle. What can you conclude?
1. They are similar (AA)
2. They are congruent
3. Nothing without side lengths
$\triangle ABC \sim \triangle DEF$ with $AB = 8$ , $BC = 7$ and $DE = 25$ . Find $EF$ .Not to scale
Which figures are always similar to each other?
1. Any two squares (for example sides 7 and 14)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 2 and 4)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 4 and 8)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 6 and 12)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 5 and 10)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 9 and 18)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 8 and 16)
2. Any two rectangles
3. Any two isosceles triangles
Which figures are always similar to each other?
1. Any two squares (for example sides 3 and 6)
2. Any two rectangles
3. Any two isosceles triangles
In $\triangle ABC$ , a line parallel to $BC$ meets $AB$ at $D$ and $AC$ at $E$ , with $AD = 5$ , $DB = 3$ and $AE = 9$ . Find $EC$ .Not to scale
In a triangle, $BC = 26$ . The segment joining the midpoints of $AB$ and $AC$ has length…
$DE \parallel BC$ with $D$ on $AB$ , $E$ on $AC$ ; $AD = 2$ , $DB = 7$ , $AE = 3$ . Find $AC$ .Not to scale
The altitude to the hypotenuse of a right triangle cuts the hypotenuse into segments 36 and 49. Find the altitude.
In a right triangle, the hypotenuse is 25 and the altitude cuts off a segment of 1 next to leg $a$ . Find $a$ .
A right triangle has legs 9 and 12. Find the hypotenuse.

Answers

$(6, 2)$
$\frac{11}{3}$
They stay the same
$27$
$100$
$36$
They are similar (AA)
$\frac{175}{8}$
Any two squares (for example sides 7 and 14)
$\frac{27}{5}$
$13$
$\frac{27}{2}$
$42$
$5$
$15$