All the solutions provided inÂ **McGraw Hill My Math Grade 5 Answer Key PDF Chapter 12 Check My Progress **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Chapter 12 Check My Progress Answer Key

**Check My Progress Page No. 921-922**

**Vocabulary Check**

**State whether each sentence is true or false.**

Question 1.

A triangle with no congruent sides is a scalene triangle.

Answer: True.

Some of the important properties of the scalene triangle are as follows:

– It has no equal sides.

– It has no equal angles.

– It has no line of symmetry.

– It has no point symmetry.

– The angles inside this triangle can be acute, obtuse or right angles.

– If all the angles of the triangle are less than 90 degrees(acute), then the centre of the circumscribing circle will lie inside a triangle.

– In a scalene obtuse triangle, the circumcenter will lie outside the triangle.

– A scalene triangle can be an obtuse-angled, acute-angled or right-angled triangle.

Question 2.

A polygon that has 4 sides and 4 angles is a pentagon.

Answer: False

A polygon that has 4 sides and 4 angles is a quadrilateral. For the pentagon, there will be 5 sides and 5 angles.

Question 3.

Sides or angles with the same measure are congruent

Answer: True.

Congruent figures are those which have sides of the same length and angles of the same measure. In other words, when one figure superimposes the other, the figures are termed congruent figures. They fit on each other exactly even when they are rotated or flipped.

Question 4.

A right triangle is a triangle with two right angles.

Answer: False

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

**Concept Check**

**Name each polygon. Determine if it appears to be regular or not regular.**

Question 5.

Answer: Pentagon, irregular

Explanation:

– Now we are going to count the sides.

– A pentagon is a geometric two-dimensional shape with five sides and five angles.

– The shape is irregular because all the interior angles and the sides are of different measures.

Question 6.

Answer: octagon, regular.

Explanation:

– Now we are going to count the sides.

– An octagon is a closed two-dimensional figure with eight sides, eight vertices and eight interior angles. If all the sides and interior angles of an octagon are of equal measure, then it is called a regular octagon otherwise an irregular octagon.

– The shape is regular because all sides are equal.

**Measure the sides of each triangle to the nearest tenth of a centimeter. Then describe the number of congruent sides.**

Question 7.

Answer:

– Now take the ruler and measure the given triangle.

–

– The shape is a triangle and it has three congruent sides.

Question 8.

Answer:

– Now take the ruler and measure the given triangle.

–

– It has 2-congruent sides.

**Problem Solving**

Question 9.

Name the polygon shown by the video game screen on the right Determine if it appears to be regular or not regular.

Answer:

– The shape of the video game screen is quadrilateral because it has 4 sides.

– The sides are not equal so it is not regular.

Question 10.

Steve has three lengths of the fence. He connects them to make a triangular pen for his dog. If the lengths are 5 meters, 6 meters, and 10 meters, what type of triangle is formed by the dog pen?

Answer: Scalene triangle

Explanation:

The above-given lengths:

6 metres, 5 metres, 10 metres.

All the sides are having different lengths. so it was a scalene triangle.

In geometry,Â Scalene Triangle is a triangle that has all its sides of different lengths.Â It means all the sides of a scalene triangle are unequal and all the three angles are also of different measures.

Therefore, the scalene triangle is formed by the dog pen.

Question 11.

Name the polygon shown by the banner at the right. Determine if it appears to be regular or not regular.

Answer:

The banner looks like a triangle shape.

To check whether it was regular or not regular we need to observe the sides. The sides are not equal so it was not regular.

Question 12.

Refer to the art in Exercise 11. Classify the triangle based on its angles.

Answer:

Triangles can be classified based on their internal angles and based on their sides.

There are three types of triangles based on internal angles: acute, right, and obtuse-angled triangles. Triangles are grouped into three groups based on the length of their sides: Scalene, Isosceles, and Equilateral triangles.

– Two sides are equal in the above-given triangle. (refer to question 11)

An isosceles triangle is a triangle with two sides of equal length.

– The legs are the two equal sides of an isosceles triangle, and the angle between them is known as the vertex angle or apex angle.

– The base angle is the side opposite the vertex angle, and the base angles are equal.

– The perpendicular drawn from the vertex made by the two equal sides bisects the base.

Question 13.

Lindsay was going to visit her grandmother, shop at the mall, and then return home. The route she took was in the shape of a triangle. The distance between each place she visited was 10 miles. What type of triangle is formed by the route she travelled?

Answer:

The shape that she took was her route is a triangle.

The distance between the miles is 10.

The triangle was formed by the route she travelled. Let it be T(R).

– Now draw a triangle with 10 miles.

–

– All sides are equal. So it is an equilateral triangle.

– Therefore, T(R) = equilateral triangle.

– An equilateral triangle has the same length on each of its three sides.

– The lengths of the sides of an equilateral triangle are the same.

– The angles of an equilateral triangle are congruent, and each is equal to 60 degrees.

– Because it has three sides, it is referred to as a regular polygon.

**Test Practice**

Question 14.

Miguel has a ladder with legs of equal length. He opened the ladder and placed it on the floor. What type of triangle is formed by the ladder and the floor?

(A) scalene triangle

(B) isosceles triangle

(C) equilateral triangle

(D) obtuse triangle

Answer: Option A is the correct answer.

If we open the ladder then the shape is a triangle.

The triangle formed when we opened the ladder is a scalene triangle. Because the two sides are equal.

– An isosceles triangle is a triangle with two sides of equal length.

**Check My Progress Page No. 947-948**

**Vocabulary Check**

**Circle the correct term or terms to complete each sentence.**

Question 1.

A (rectangular prism, triangular prism) is a three-dimensional figure with six rectangular faces and eight vertices.

Answer:

– A rectangular prism has 6 faces, 12 edges and 8 vertices

– The top and base of the rectangular prism are always a rectangle

– Like a cuboid, it also has three dimensions, i.e., length width and height

– Pairs of opposite faces are identical or congruent

– For a right rectangular prism, the lateral faces are rectangle

– For oblique rectangular prims, the lateral faces are parallelogram

– It has a rectangular cross-section

– It looks exactly like a cuboid

Question 2.

A (rectangle, rhombus) is a parallelogram with all sides congruent.

Answer:

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.

Question 3.

A(n) (vertex, edge) of a three-dimensional figure is where two faces meet.

Answer:

The line segment which acts as an interface between two faces is called an edge. Sometimes it is also described as the line segment joining two vertices.

Question 4.

A (prism, trapezoid) has at least three faces that are rectangles.

Answer:

A prism has a solid shape consisting of two identical ends (such as a triangle, square, rectangle, etc.), flat faces or surfaces and a uniform cross-section across its length. The cross-section looks like a triangle hence called a triangular prism. The shape of the prism does not have any curve. Therefore, a prism can have square, rectangular, pentagonal and other polygon shapes but not circular shapes.

**Concept Check**

**Describe the attributes of each quadrilateral. Then classify the quadrilateral.**

Question 5.

Answer:

The name of the shape is a parallelogram

Attributes:

– The opposite sides of a parallelogram are equal in measurement and they are parallel to each other.

– The opposite angles of a parallelogram are equal.

– The sum of interior angles of a parallelogram is equal to 360Â°.

– The consecutive angles of a parallelogram should be supplementary (180Â°).

Question 6.

Answer:

The name of the shape is quadrilateral

Attributes:

– A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.

– No sides are congruent and parallel. So it is not regular.

– It is an arrow in shape.

Question 7.

Circle the quadrilateral(s) that have all the attributes of a rhombus.

trapezoid

square

parallelogram

rectangle

Answer:

Check out all the attributes of the quadrilaterals.

Square: A square is a four-sided polygon that has all its sides equal in length, and all the angles are equal to 90 degrees. The length of the diagonals is also equal.

Rhombus: Â A rhombus is also a four-sided polygon, and all sides are equal in length. The opposite angles of a rhombus are equal, and the diagonals bisect each other at 90 degrees.

Question 8.

Circle the quadrilateral(s) that have all the attributes of a rectangle.

parallelogram

square

trapezoid

rhombus

Answer:

Rectangle: A quadrilateral whose opposite sides are equal and parallel and all the interior angles equal to 90Â° is defined as Rectangle. Diagonals of rectangles bisect each other. Note that all the rectangles are parallelograms, but the parallelograms are not rectangles.

Parallelogram: A quadrilateral whose opposite sides are equal and parallel is called a parallelogram. Opposite angles of a Parallelogram are equal, and its diagonals bisect each other.

Square: A quadrilateral that has all sides equal and opposite sides parallel and all interior angles equal to 90Â° is called a square. Diagonals of squares bisect each other perpendicularly. Note that all squares are rhombus but not vice-versa.

Trapezium: A trapezium is a quadrilateral that has one pair of opposite sides parallel. In a regular trapezium, non-parallel sides are equal, and its base angles are equal.

Rhombus: A quadrilateral that has all sides equal and opposite sides parallel is called Rhombus Opposite angles of a rhombus are equal, and diagonals of the Rhombus bisect each other perpendicularly. Note all rhombus are parallelograms, but the reverse of this is not true.

**Describe the faces, edges, and vertices of each three-dimensional figure. Then Identify It.**

Question 9.

Answer:

The number of faces = 6

The number of edges = 12

The number of vertices = 8

The shape is a rectangular prism.

Rectangular prism: A prism with rectangular bases is called a rectangular prism. A right rectangular prism is a prism that has six faces that are rectangles, and all angles are right angles.

Question 10.

Answer:

The number of faces = 5

The number of edges = 9

The number of vertices = 6

– The name of the shape is a triangular prism.

– It has two triangular bases and three rectangular sides

– If the triangular bases are equilateral and the other faces are squares, instead of a rectangle, then the triangular prism is said to be semiregular

**Problem Solving**

Question 11.

Kendra’s xylophone is in the shape of the trapezoid shown at the right Describe any parallel, perpendicular, or congruent sides of the xylophone.

Answer:

A trapezoid will always have two parallel sides.

There are 2 right angles instead of 4.

Congruent refers to the same as equal or identical. Because two sides are congruent, their lengths are equal.

Question 12.

Garrett cut a piece of cheese to eat for a snack. The cheese is a prism with 3 faces that are rectangular and 2 that are triangular. What kind of figure is it?

Answer:

The shape is a triangular prism.

AÂ triangular prismÂ is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

– It has a total of 9 edges, 5 faces, and 6 vertices (which are joined by the rectangular faces).

– It has two triangular bases and three rectangular sides

– If the triangular bases are equilateral and the other faces are squares, instead of a rectangle, then the triangular prism is said to be semiregular.

**Test Practice**

Question 13.

Which is riot a true statement?

(A) All squares are parallelograms.

(B) Some rhombi are squares.

(C) All rectangles are squares.

(D) All rectangles are parallelograms.

Answer: Option C is the correct answer.

Explanation:

Option A: Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms. So it is a true statement.

Option B: A rhombus is a quadrilateral which has all sides congruent. It can have oblique angles or right angles. A rhombus with right angles is a square. So it is a true statement.

Option C: A Square is a special kind of rectangle. Every Square is a rectangle, but not every rectangle is a square. Conclusion: a square is always a rectangle, but a rectangle is not always a square. However, it is important to keep in mind that even though all squares are rectangles, not all rectangles are squares. So it is not a true statement.

Option D: A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. So it is a true statement.