Train Up Mathematics 1 (S1 to S2)24

Quick Review1. Points, Lines and Planes

E.g., A and B are points.AB and BC are line segments.ABCD is a plane.

2. Types of Angles

Right angle（直角）

Obtuse angle（鈍角）

3. Parallel Lines and Perpendicular Lines

4. Plane FiguresA. Circles

Introduction to Geometry5

Ans: 1. F 2. T 3. F 4. F 5 (a) acute (b) right (c) reflex

Determine whether each of the following is true (1 – 4).1. In the figure, c is an obtuse angle.

T / F

2. is an isosceles triangle. T / F

3. Circle is a kind of polygon. T / F

4. B o t h p r o t r a c t o r a n d a p a i r o f compasses can be used to measure an angle. T / F

5. In the figure,

a is a/an (a) angle, b is a/an (b) angle and c is a/an (c) angle.

Concept Check

Introduction to Geometry 25

B. Triangles(a) Types of triangles classified by (b) Types of triangles classified by the the sizes of their interior angles lengths of sides of triangles

(c) Angle sum of a triangle

∠A + ∠B + ∠C = 180° (∠ sum of D)

C. Polygons

Regular polygons are polygons with equal sides and equal angles.

5. SolidsA. Polyhedra

A polyhedron is a solid with polygonal faces.

B. Cross-section of a Solid

Prisms have uniform cross-sections such as the one shown above.

Mistake HuntIn the figure, ABCD is a rectangle. Write down the names of all right-angled triangles.Solution:

DADE, DCDE, DBCE, DABE,DABD, DACD, DBCD, DABC

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➥

Level-up Practice Q. 14

We should not determine the lengths and sizes of angles visually. Hence the correct solution is as follows:DABD, DACD, DBCD, DABC

! !

Train Up Mathematics 1 (S1 to S2)26

What's Wrong?

Level-up PracticeMultiple-choice Questions

1. In the figure, AMB is a straight line. Which of the following is an obtuse angle? A. ∠AMB B. ∠BMC

C. ∠CMD D. ∠BMD

2. A, B, C and D are points on a plane. AB and AC are perpendicular to each other and ∠CAD is an acute angle. Which of the following statements must be correct?

A. ∠ABC = 90° B. ∠BAC = 90° C. ∠BAD is an obtuse angle. D. ∠BAD is a reflex angle.

3. In DABC, AB = AC = 4 cm and BC = 5 cm. It must beA. a scalene triangle. B. a right-angled triangle. C. an obtuse-angled triangle. D. an isosceles triangle.

4. Which of the following statements is/are correct? I. All rectangles are equiangular polygons. II. All squares are equilateral polygons and equiangular polygons. III. All regular hexagons are equilateral polygons but not equiangular polygons. A. I only B. I and II only C. I and III only D. II and III only

5. Which of the following has a uniform cross-section in the shape of a square? A. B.

C. D.

Study the following and determine whether the solution of the question is correct. If it is not, correct the solution.The figure shows a quadrilateral ABCD. Write down all isosceles triangles.

Solution:

DABD and DBCD

Introduction to Geometry 27

Basic Questions Find the unknowns in the following figures (6 – 8).6. 7. 8.

x = y = z =

9. Referring to the figure, (a) name the line segment that is parallel to BC, (b) find the total length of the line segments, (c) find the shortest distance between A and F.

Find the unknowns in the following figures (10 – 12).10. 11. 12.

13. Determine whether each of the following solids is a polyhedron. (a) (b) (c) (d)

Enhanced Questions 14. In the figure, ABCD is a square and BC = ED = EC. (a) Name all the equilateral triangles.

(b) Name two isosceles triangles.

(c) Name all the right-angled trangles.

15. In the figure, AOB and COD are straight lines. Write down the names of all angles corresponding to each of the following types of angles.

(a) Acute angle (b) Right angle (c) Obtuse angle

Train Up Mathematics 1 (S1 to S2)28

Self-assessment1. It is given that ABC is a straight line and ∠ABD is an acute angle. Draw a figure to represent it

and mark down an obtuse angle x and a reflex angle y in the figure.

2. In the figure, ADB is a straight line. Find the unknowns.

16. A capsule is shown below.

AB = 6 unitsCD = 2 units

Draw the cross-section of the capsule when the capsule is cut along (a) AB; (b) the dotted line passing through C and D.

17 . In each of the following figures, determine whether the solid has a uniform cross-section. If it has, name the shape of the uniform cross-section of the solid.

(a)

(b)

(c) (d)

18. The figure shows the diagram of a cuboid:Referring to the sketch shown on the right, draw a pyramid with rectangular base on the same diagram.

Introduction to Geometry 29

Internet Adventure

Knowledge Extension Corner

3. The figure shows a dice. Draw the cross-section of the dice.

We may classify some special quadrilaterals as follows. Kite: with 2 distinct pairs of equal adjacent sides Trapezium: with only 1 pair of parallel sides Parallelogram: with 2 pairs of parallel sides Square: with 4 right angles and 4 equal sides Rectangle: with 4 right angles Rhombus: with 4 equal sidesThese quadrilaterals have many beautiful geometric properties. We will study them in details in S3.

Work it out 1. Quadrilateral A has two sides which will not intersect with each other when they are

extended. Do you know what kind of quadrilateral is it?2. Quadrilateral P has 4 equal sides, while quadrilateral Q has 4 right angles. Quadrilateral R

has all properties of P and Q. Do you know what kind of quadrilateral is quadrilateral R?

Platonic Solids

There are 5 kinds of Platonic solids. Do you know their shapes? You may visit the following website for more details.

http://www.mathsisfun.com/platonic_solids.html