# Math in Focus Grade 5 Chapter 13 Practice 3 Answer Key Right, Isosceles, and Equilateral Triangles

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 3 Right, Isosceles, and Equilateral Triangles provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 13 Practice 3 Answer Key Right, Isosceles, and Equilateral Triangles

Complete. ABC and EFG are right triangles.

Question 1.

m∠B =___
m∠A + m∠C = ___
= ____
m∠B =90°
m∠A + m∠C = 90°
Explanation:
Properties of Right – Angled Triangle

• One angle of the triangle always measures 90degree.
• The hypotenuse is the longest side of the right-angle triangle.
• The side that is opposite to the 90degree angle is the hypotenuse.
• The Sum of two interior angles of the right-angled triangle is always 90degree.

Question 2.

m∠E = ___
m∠F + m∠G = ___
m∠E = 90°
m∠F + m∠G = 90°

Explanation:
Properties of Right – Angled Triangle

• One angle of the triangle always measures 90°.
• The hypotenuse is the longest side of the right-angle triangle.
• The side that is opposite to the 90° angle is the hypotenuse.
• The Sum of two interior angles of the right-angled triangle is always 90degree.

Measure the angles of the triangle. Then fill in the blanks.

Question 3.

m∠A _____
m∠B ______
m∠C ______
m∠A + m∠C ______
m∠B = 90°

m∠C = 40°

m∠A = 50°
Explanation:
Sum of angles in a triangle are 180°
40 + 90 = 130
180 – 130 = 50
m∠A = 50°
m∠A + m∠C = 50° + 40° = 90°

These triangles are not drawn to scale. Identify and shade the right triangles.

Question 4.

Explanation:

Properties of Right – Angled Triangle
• One angle of the triangle always measures 90°.
• The hypotenuse is the longest side of the right-angle triangle.
• The side that is opposite to the 90° angle is the hypotenuse.
• The Sum of two interior angles of the right-angled triangle is always 90degree.

These triangles are not drawn to scale. Find the unknown angle measures.

Question 5.
Find the sum of the measures of ∠A and ∠B.

∠A  + ∠B = 90°
Explanation:
Properties of Right – Angled Triangle

• One angle of the triangle always measures 90°.
• The hypotenuse is the longest side of the right-angle triangle.
• The side that is opposite to the 90° angle is the hypotenuse.
• The Sum of two interior angles of the right-angled triangle is always 90degree.

Question 6.
Find the measure of ∠C.

33°
Explanation:
Properties of Right – Angled Triangle

• The Sum of two interior angles of the right-angled triangle is always 90degree.
So in right angle triangle, Sum of other two angles is 90°.
So ∠C = 90 – 57 = 33

Question 7.
Find the measure of ∠ADC and ∠ABC.

∠ABC =28°
Explanation:
In Triangle DAB, ∠DAB =90°
In Triangle ABC, ∠ACB=90°
In Triangle ACD, ∠ACD=90°
and ∠DAC=28°
So ∠ADC = 180° -(∠ACD +∠DAC) = 180° -(90°+28°) = 180° -(118°) =62°
∠BAC = ∠DAB – ∠DAC = 90° -28° = 62°
∠ABC =180° -(∠ACB +∠BAC) = 180° -(90°+62°) = 180° -(152°) =28°

Question 8.
Find the measures of ∠EGF and ∠DGE.

∠EGF  =64°
∠DGE = 26°
Explanation:
In Triangle DGF, ∠DGF=90°
In Triangle GEF, ∠GEF=90° and ∠EFG=26°
In Triangle DEG, ∠DEG=90°
So ∠EGF= 180° -(∠GEF+∠EFG) = 180° -(90°+26°) = 180° -(116°) =64°
∠DGE= ∠DGF- ∠EGF= 90° -64° = 26°
Complete. XYZ and PQR are isosceles triangles.

Question 9.

Which two sides are of equal length?
________
Which two angles have equal measures?
_________
XY and XZ  sides are equal length.
∠Z and ∠Y angles have equal measures.
Explanation:

An Isosceles Triangle has the Following Properties:
• It has two sides of equal length.
• The angles opposite to equal sides are equal in measure

Question 10.

Which two sides are of equal length?
_________
Which two angles have equal measures?
________
PR and QR sides are of equal length.
∠P and ∠Q angles have equal measures.
Explanation:
An Isosceles Triangle has the Following Properties:

• It has two sides of equal length.
• The angles opposite to equal sides are equal in measure

These triangles are not drawn to scale. Find the unknown angle measures.

Question 11.

Explanation:
The properties of a triangle are:

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. So,

1.  180 – (46 + 86) = 48
2. 180 – (75+74) = 31
3. 180  – (64 +52) = 64
4. 180 – (90 + 30 ) = 60
5. 180 – (80 + 80 ) = 20

These triangles are not drawn to scale. Find the unknown angle measures.

Question 12.
Find the measure of ∠F.

∠F = 74°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180°.
∠D + ∠F = 180 – 53 = 127 °

An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure
So ∠D = ∠E Then ∠D = 53 °
then ∠F = 127 – 53 =74°

Question 13.
Find the measure of ∠C.

∠C  =72°

Explanation:
The property of a triangle is: The sum of all internal angles of a triangle is always equal to 180°.
∠C + ∠B = 180 – 36 = 144°
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure
So ∠C = ∠B Then 144/2 =72°
then ∠C  =72°

Question 14.
Find the measure of ∠TRS.

∠TRS = 180 – (∠RST+∠RTS)=180 – (20+90) = 70°
Explanation:
Triangle URS is a Isosceles Triangle.
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then
∠U= ∠S = 20°
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180°.
In Triangle TRS ,
∠RST = 20°
∠RTS = 90°
∠TRS = 180 – (∠RST+∠RTS)=180 – (20+90) = 70°

Question 15.
Find the measure of ∠d.

∠d =  172°
Explanation:
Triangle WXY is a Isosceles Triangle.
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then
then ∠W= ∠Y
Triangle WXZ a Right angle Triangle.
then ∠WZX = 90°
∠WXZ=86°
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180°.
In Triangle WZX,
∠XWZ = 180 – (∠WZX+∠WXZ )=180 – (90+86) = 4°
In Triangle WXY , ∠W= ∠Y  = 4°
∠d = 180 – (4+4) = 172°

Complete. Use your protractor and centimeter ruler to measure the sides and angles. Which figure is an equilateral triangle? Check the box.

Question 16.

AB = __ cm
BC = __ cm
AC = ___ cm
m∠A = ___
m∠B = ___
m∠C = ____

Question 17.

XY = __ cm
YZ = __ cm
XZ = ___ cm
m∠X = ___
m∠Y = ___
m∠Z = ____

Explanation:
XY = 4 cm
YZ = 4 cm
XZ = 4 cm
m∠X = 60°
m∠Y = 60°
m∠Z = 60°
Explanation:
The angles and sides are equal

Complete. ABC is an equilateral triangle.

Question 18.
Which angles have measures equal to the measure of ∠A?
∠A = ∠B = ∠C
Explanation:

Properties of an Equilateral Triangle
• Three sides are equal.
• Three angles are equal i.e 60° each.

Question 19.
Which sides have lengths equal to the length of $$\overline{A B}$$?
$$\overline{A B}$$= $$\overline{B C}$$ = $$\overline{A C}$$
Explanation:

Properties of an Equilateral Triangle
• Three sides are equal.
• Three angles are equal i.e 60° each.

Question 20.
What can you say about the angles of triangle ABC ?
All angles are equal and 60° each.

Explanation:

Properties of an Equilateral Triangle
• Three sides are equal.
• Three angles are equal i.e 60° each.

These triangles are not drawn to scale. Identify and shade the equilateral triangles.

Question 21.

Explanation:
Properties of an Equilateral Triangle

• Three sides are equal.
• Three angles are equal i.e 60° each.

These triangles are not drawn to scale. Find the unknown angle measures.

Question 22.
Find the measure of ∠Q.

∠Q = 60°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180°.
∠Q  = 180 – ∠P + ∠R = 180 – 60 + 60 = 60°

Question 23.
Find the measures of ∠Y and ∠Z

∠Y =∠Z= 60°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180°.
∠Z + ∠Y  = 180 – ∠X  = 180 – 60  = 120°
As per diagram Triangle XYZ is a Isosceles Triangle.
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then
∠Y =∠Z
then ∠Y =∠Z= 120°/2 = 60°

These triangles are not drawn to scale. Find the unknown angle measures.

Question 24.
WX = XY = YW. Find the measure of ∠d.

Explanation:
WX = XY = YW So Triangle WXY is a Equilateral Triangle So Three angles are equal
∠WXY = 60°
∠XWY= 60°
∠WYX= 60°
So In Triangle XYZ,
∠ZXY= 60°
∠XZY= 90°
∠XYZ= 180 – 90 + 60=30°
∠d = ∠WYX -∠XYZ  =60 – 30 =30°

Question 25.
Find the measure of ∠e.

∠e = 120°
Explanation:
∠LON = 90° given
As the triangle is equalateral the angles are equal
so the measure of ∠LOE = 60°
∠LMO = 60°
NOM triangle is an isosceles triangle
90 – 60 = 30°
∠MON = 30°
∠OMN = 30°
30° + 30° = 60°
180° – 60° = 120°
∠e = 120°

Question 26.
Triangle PQR is an equilateral triangle. Triangle PST is an isosceles triangle. The measures of ∠a, ∠b, and ∠c are the same. Find the measure of ∠d.

∠d. = 80°
Explanation:
Triangle PQR is an equilateral triangle.
In equilateral triangle all angles are equal
sum of angles in a triangle are 180°
Triangle PST is an isosceles triangle.
The measures of ∠a, ∠b, and ∠c are the same.
so, ∠a, ∠b, and ∠c = 60°
20° + 20° + 20° = 60°
In isosceles triangle
The isosceles triangle property states that when two sides are equal, the base angles are also equal
so, 180° – 20° = 160°
80° + 80 °= 160°
∠d. = 80°