Sofia draws these triangles and said, I think my two triangles are congruent. Without knowing the lengths of any of the sides, how do you know that Sofia is incorrect?

Given, If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then the triangles are congruent. We know that the sum of the internal angles of a triangle is 180 ° Let's take the first triangle and find the missing angle, ∠ x + 57 ° + 42 ° = 180 ° ⇒ ∠ x = 81 ° Now take the second triangle and find the missing angle. ∠ Y + 84 ° + 42 ° = 180 ° ⇒ ∠ Y = 54 ° We can see that the corresponding angles are not the same for the given triangles. Therefore, the triangles were drawn by Sofia are not congruent.

Match the properties ( a to d ) of each 3 D shape with its name ( A to D ) and picture ( i to i v ) . Properties Name of shape Picture of shape I have two faces that are congruent circles. I have one curved surface. I have two edges and no vertices. Tetrahedron I have four faces. All of my faces are congruent equilateral triangles. I have six edges and four vertices Pentagonal prism I have only one curved surface. I have no edges or vertices Cylinder I have seven faces. Two of my faces are congruent pentagons and the other faces are congruent rectangles. I have 15 edges and ten vertices Sphere

Properties Name of shape Picture of shape I have two faces that are congruent circles. I have one curved surface. I have two edges and no vertices. Cylinder I have four faces. All of my faces are congruent equilateral triangles. I have six edges and four vertices Tetrahedron I have only one curved surface. I have no edges or vertices Sphere I have seven faces. Two of my faces are congruent pentagons and the other faces are congruent rectangles. I have 15 edges and ten vertices Pentagonal prism

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Lower Secondary Stage 7

IMPORTANT

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These two triangles are congruent.

Write down the length of the side $Y Z$ in centimeters.

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Important Questions on Shapes and Symmetry

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Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.3>Q 5

These two triangles are congruent.
Question Image

Write down the size of $U V W$ in degrees..

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Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.3>Q 5

These two triangles are congruent.
Question Image

Write down the size of $U W V$ in degrees.

EASY

Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.3>Q 5

These two triangles are congruent.
Question Image

Write down the size of $Y X Z$ in degrees.

EASY

Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.3>Q 6

Sofia draws these triangles and said, I think my two triangles are congruent.

Question Image

Without knowing the lengths of any of the sides, how do you know that Sofia is incorrect?

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Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.3>Q 8

Sofia and Zara are looking at these two triangles.

Question Image

Sofia says: I think these two triangles are congruent because the corresponding sides are the same length.

Zara says: you can not tell if these triangles are congruent because you do not know any of the angles.

Who is correct, Sofia or Zara? Explain your answer.

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Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.4>Q 1

Match the properties ( $a$ to $d$ ) of each $3 D$ shape with its name ( $A$ to $D$ ) and picture $(i$ to $i v)$ .

Properties	Name of shape	Picture of shape
I have two faces that are congruent circles. I have one curved surface. I have two edges and no vertices.	Tetrahedron
I have four faces. All of my faces are congruent equilateral triangles. I have six edges and four vertices	Pentagonal prism
I have only one curved surface. I have no edges or vertices	Cylinder
I have seven faces. Two of my faces are congruent pentagons and the other faces are congruent rectangles. I have $15$ edges and ten vertices	Sphere

EASY

Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.4>Q 2

Write down the properties that characterise a cube. You must include information about the faces, edges and vertices.

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Lower Secondary Stage 7

IMPORTANT

Cambridge Lower Secondary Mathematics Learner's Book 7 Second Edition Digital Access>Chapter 8 - Shapes and Symmetry>Exercise 8.4>Q 7

The top view, front view and side view of 3D shape is given. Write the name the shape.

Top view	Front view	Side view

These two triangles are congruent. Write down the length of the side YZ in centimeters.

Important Questions on Shapes and Symmetry

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These two triangles are congruent.

Write down the length of the side $Y Z$ in centimeters.