Geometry and measures, Year 7: more practice

On the vertex (the corner) of the angle

提示It goes where the two arms meet.

为什么The baseline of the protractor must also lie along one arm, so the other arm points to the reading on the scale.

55° — read the other scale (180° − 125°)

提示An acute angle is less than 90°.

为什么Protractors have two scales running in opposite directions. Start from 0° on the arm you are lined up with; 125° is the reading from the other end, and 180° − 125° = 55°.

Compasses, drawing two arcs

提示Draw the 7 cm base first, then you need two curves that cross.

为什么From one end of the base draw an arc of radius 5 cm, and from the other end an arc of radius 6 cm. They cross at the third vertex.

SAS (side, angle, side)

提示The known corner sits between the two lengths.

为什么SAS fixes one triangle only. The angle must lie between the two known sides; a given angle that is not between them can give two different triangles.

3

提示Volume is length × width × height, so work backwards by dividing.

为什么The base area is 5 × 4 = 20 cm², and 60 ÷ 20 = 3. Check: 5 × 4 × 3 = 60.

No, it has none

提示Imagine folding it along a diagonal or through the midpoints of opposite sides.

为什么Folding along a diagonal makes the two halves match in size but the corners do not land on each other. It does have rotational symmetry of order 2.

2

提示Count how many positions in a full turn look exactly the same.

为什么A rectangle fits onto itself after a half turn and after a full turn, so its order is 2.

(−3, 2)

提示The y-axis is vertical: which way does the point move, and does its height change?

为什么The image is the same distance from the mirror line on the other side, and 2 up as before. Reflecting in the y-axis changes the sign of x.

146

提示One centimetre is split into ten small divisions on a ruler.

为什么1 cm = 10 mm, so 14.6 × 10 = 146 mm. The 0.6 cm is six of the small divisions.

A chord

提示It is not a radius or a diameter.

为什么A chord joins any two points on the circumference. The longest chord passes through the centre and is a diameter.