One line of symmetry Isosceles triangle has only one line of symmetry.

Contents

- 1 Can isosceles triangle have 3 lines of symmetry?
- 2 Is there a line of symmetry in an isosceles triangle?
- 3 Are all 3 sides of an isosceles triangle the same?
- 4 Which quadrilateral can have up to 4 lines of symmetry?
- 5 Which shape has 4 lines of symmetry?
- 6 Which has 5 lines of symmetry?
- 7 Is there a triangle with 3 lines of symmetry?
- 8 Can a triangle have 3 lines of symmetry?
- 9 Can an isosceles triangle have 3 congruent angles?

## Can isosceles triangle have 3 lines of symmetry?

Answer and Explanation: An isosceles triangle has one line of symmetry. However, if the isosceles triangle is also an equilateral triangle, then it has three lines of symmetry. An isosceles triangle is defined as a triangle with two sides of equal length.

## Is there a line of symmetry in an isosceles triangle?

Answer: An isosceles triangle has 1 line of symmetry. The triangle also has 2 equal interior sides.

### Which triangle has 2 lines of symmetry?

No triangle can be formed which has exactly two lines of symmetry.

#### What shape has 3 lines of symmetry?

Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right. Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

This type of symmetry is called line symmetry, Any isosceles triangle has line symmetry. The dashed lines represent lines of symmetry, and each shape is said to be symmetrical about this line. The following all have line symmetry: A shape can have more than one line of symmetry. Thus a rectangle has two lines of symmetry, an equilateral triangle has three lines of symmetry, and a square has four. A circle has an infinite number of lines of symmetry since it can be folded about any diameter. Only eight of the possible lines of symmetry are indicated below. Some shapes, such as a scalene triangle, have no lines of symmetry – it is not possible to fold the shape about a line so that the two halves fit exactly on top of one another.

## Are all 3 sides of an isosceles triangle the same?

From Wikipedia, the free encyclopedia

Isosceles triangle | |
---|---|

Isosceles triangle with vertical axis of symmetry | |

Type | triangle |

Edges and vertices | 3 |

Schläfli symbol | ( ) ∨ |

Symmetry group | Dih 2,, (*), order 2 |

Properties | convex, cyclic |

Dual polygon | Self-dual |

In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case,

Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids, The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics, Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings.

The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base.

## Which quadrilateral can have up to 4 lines of symmetry?

Solution – The lines of symmetry for each of the four quadrilaterals are shown below: When a geometric figure is folded about a line of symmetry, the two halves match up so if the students have copies of the quadrilaterals they can test lines of symmetry by folding. For the square, it can be folded in half over either diagonal, the horizontal segment which cuts the square in half, or the vertical segment which cuts the square in half.

- So the square has four lines of symmetry.
- The rectangle has only two, as it can be folded in half horizontally or vertically: students should be encouraged to try to fold the rectangle in half diagonally to see why this does not work.
- The trapezoid has only a vertical line of symmetry.
- The parallelogram has no lines of symmetry and, as with the rectangle, students should experiment with folding a copy to see what happens with the lines through the diagonals as well as horizontal and vertical lines.

The lines of symmetry indicated are the only ones for the figures. One way to show this is to note that for a quadrilateral, a line of symmetry must either match two vertices on one side of the line with two vertices on the other or it must pass through two of the vertices and then the other two vertices pair up when folded over the line.

#### Which triangle has 3 lines of symmetry?

Yes, an equilateral triangle has exactly three lines of symmetry.

### Which triangle has 1 line of symmetry?

Isosceles triangle has only one line of symmetry.

### Why can’t a triangle have 2 lines of symmetry?

Answer and Explanation: No, a triangle cannot have 2 lines of symmetry. The number of lines of symmetry a triangle can have depends on the type of triangle. Specifically, it’s the relationship between the three different sides of the triangle that determines its number of lines of symmetry.

#### Why can’t triangles have 2 lines of symmetry?

Line symmetry of triangles – An isosceles triangle has two equal sides and two equal angles. This means that it is symmetrical: The dotted, vertical line divides the triangle into two halves, and each half is a mirror image of the other. If we were to fold the shape along the line, the two halves would match exactly. The line goes from the top vertex of the triangle down to the centre of the base. In a scalene triangle, all the sides and angles are different, so it is not possible to draw a line that divides the shape into two symmetrical halves. We say that the shape has no lines of symmetry. Let’s look at an equilateral triangle : In an equilateral triangle, all three sides and angles are equal. We can draw a line of symmetry from the top vertex to the centre base, similar to the isosceles triangle. We can also draw lines of symmetry from the other two vertices to the opposite side.

### What shape has 0 lines of symmetry?

A scalene triangle, a parallelogram, and a trapezium are examples of shapes that have no lines of symmetry.

### Do all triangles have 3 lines of symmetry?

IM Commentary – The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry. A scalene triangle is a triangle with no lines of symmetry while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections. A word has been added at the end of the solution about why there are not other lines of symmetries for these triangles: this has been inserted in case this topic comes up in a class discussion but the focus should be on identifying the proper lines of symmetry.

## Which shape has 4 lines of symmetry?

A square has four lines of symmetry.

### What is the rule for isosceles triangles?

Isosceles Triangle Properties – An Isosceles Triangle has the following properties:

- Two sides are congruent to each other.
- The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.
- The two angles opposite to the equal sides are congruent to each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.
- The angle which is not congruent to the two congruent base angles is called an apex angle.
- The altitude from the apex of an isosceles triangle bisects the base into two equal parts and also bisects its apex angle into two equal angles.
- The altitude from the apex of an isosceles triangle divides the triangle into two congruent right-angled triangles.
- Area of Isosceles triangle = ½ × base × altitude
- Perimeter of Isosceles triangle = sum of all the three sides

Example: If an isosceles triangle has lengths of two equal sides as 5 cm and base as 4 cm and an altitude are drawn from the apex to the base of the triangle. Then find its area and perimeter.

- Solution : Given the two equal sides are of 5 cm and base is 4 cm.
- We know, the area of Isosceles triangle = ½ × base × altitude
- Therefore, we have to first find out the value of altitude here.
- The altitude from the apex divides the isosceles triangle into two equal right angles and bisects the base into two equal parts. Thus, by Pythagoras theorem,
- Hypotenuse 2 = Base 2 + Perpendicular 2
- Therefore,
- \(\begin Perpendicular =\sqrt \end \)
- \(\begin Altitude =\sqrt \end \)
- \(\begin =\sqrt \end \)
- = √21
- So, the area of Isosceles triangle = ½ × 4 × √21 = 2√21 cm 2
- Perimeter of Isosceles triangle = sum of all the sides of the triangle
- = 5 + 4 +5 cm
- = 14 cm

#### Are two sides of an isosceles triangles always equal?

Isosceles Triangle – Definition, Properties, Angles, Area, Formula, Examples An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure. In geometry, is a three-sided polygon that is classified into three categories based on its sides, such as:

- Scalene triangle (All three sides are unequal)
- Isosceles triangle (Only two sides are equal)
- Equilateral triangle (All three sides are equal)

In this article, we will learn the properties and formulas related to the isosceles triangle, in detail, along with examples.

### Is ABC an isosceles triangle?

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig.7.32). Show that (i) ΔABE ≅ ΔACF (ii) AB = AC, i.e., ABC is an isosceles triangle. – NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.2 Question 4 Summary: If ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal, then ΔABE ≅ ΔACF using AAS congruency and AB = AC i.e., ABC is an isosceles triangle.

ABC and DBC are two isosceles triangles on the same base BC (see Fig.7.33). Show that ∠ABD = ∠ACD. ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig.7.34). Show that ∠BCD is a right angle. ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C. Show that the angles of an equilateral triangle are 60° each.

#### Which quadrilateral has no line of symmetry?

Parallelogram. A parallelogram has no lines of symmetry.

#### Is A rhombus a parallelogram?

Solution: Parallelogram and Rhombus are four-sided polygons also known as quadrilaterals having four sides and four angles. A parallelogram is a four-sided convex polygon with opposite sides parallel and equal with opposite angles being equal. A rhombus is a special type of parallelogram where all the sides are equal in measure with opposite sides being parallel.