Use the triangle above to answer the questions that follow. (a) Is this triangle scalene, isosceles, or…

Question

Use the triangle above to answer the questions that follow. (a) Is this triangle scalene, isosceles, or equilateral? (b) Name two sides of the triangle that are equal. (c) What is the length of JK? (d) Name two equal angles in this triangle. (e) What is the size of angle J and angle L?

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Here are the solutions to your geometry questions:

2.4.1 Use the triangle above to answer the questions that follow:

(a) Is this triangle scalene, isosceles, or equilateral?

Observe the tick marks on the sides of triangle JKL.
Sides JK and KL both have a single tick mark, indicating they are equal in length.
A triangle with two equal sides is an isosceles triangle.
**Answer:** $\boxed{\text{Isosceles}}$
- (b) Name two sides of the triangle that are equal.
Identify the sides with identical tick marks.
**Answer:** $\boxed{\text{JK and KL}}$
- (c) What is the length of JK?
The length of KL is given as 6 cm.
Since JK = KL (from the tick marks), the length of JK is also 6 cm.
**Answer:** $\boxed{\text{6 cm}}$
- (d) Name two equal angles in this triangle.
In an isosceles triangle, the angles opposite the equal sides are equal.
The side JK is opposite angle L, and the side KL is opposite angle J.
Since JK = KL, then $\angle J = \angle L$ .
Answer: $\boxed{\text{Angle J and Angle L}}$
- (e) What is the size of angle J and angle L?
The square symbol at angle K indicates that $\angle K = 90^\circ$ .
The sum of angles in a triangle is $180^\circ$ .
So, $\angle J + \angle L + \angle K = 180^\circ$ .
Since $\angle J = \angle L$ and $\angle K = 90^\circ$ , we have $2 \times \angle J + 90^\circ = 180^\circ$ .

Solve for $\angle J$

$$
2 \times \angle J = 180^\circ - 90^\circ
$$
$$
2 \times \angle J = 90^\circ
$$
$$
\angle J = \frac{90^\circ}{2}
$$
$$
\angle J = 45^\circ
$$

Therefore, $\angle L = 45^\circ$ .
**Answer:** $\boxed{\text{Angle J} = 45^\circ, \text{Angle L} = 45^\circ}$
2.5.1 Use what you know about the sides and angles of quadrilaterals to answer the following questions:
- (a) What type of quadrilateral is ABCD?
Observe the tick marks and arrows on quadrilateral ABCD.
Sides AB and DC have single tick marks and arrows, indicating they are equal and parallel.
Sides AD and BC have double tick marks and arrows, indicating they are equal and parallel.
A quadrilateral with two pairs of opposite sides that are both equal and parallel is a parallelogram.
**Answer:** $\boxed{\text{Parallelogram}}$
- (b) Name a side equal to AB.
Identify the side with the same tick mark as AB.
**Answer:** $\boxed{\text{DC}}$
- (c) What is the length of BC?
Side AD has a double tick mark and its length is given as 2.5 m.
Side BC also has a double tick mark, indicating it is equal to AD.
**Answer:** $\boxed{\text{2.5 m}}$
2.5.2
- (a) What type of quadrilateral is EFGH?
Observe the tick marks on quadrilateral EFGH.
Sides HE and GH both have a single tick mark, indicating they are equal. Side EF has a double tick mark, and side FG has a length of 35 cm.
In a kite, two pairs of adjacent sides are equal.
From the markings, HE = GH. The shape also implies EF = FG.
Answer: $\boxed{\text{Kite}}$
- (b) What are the lengths of the sides EF and GH?
From the tick marks, HE = GH.
The length of HE is given as 16 cm. So, GH = 16 cm.
In a kite, the other pair of adjacent sides are also equal, so EF = FG.
The length of FG is given as 35 cm. So, EF = 35 cm.
Answer: $\boxed{\text{EF} = 35 \text{ cm, GH} = 16 \text{ cm}}$

Use the triangle above to answer the questions that follow. (a) Is this triangle scalene, isosceles, or equilateral? (b) Name two sides of the triangle that are equal. (c) What is the length of JK? (d) Name two equal angles in this triangle. (e) What is the size of angle J and angle L?

Step-by-step solution

Observe the tick marks on the sides of triangle JKL.

A triangle with two equal sides is an isosceles triangle.

Identify the sides with identical tick marks.

The length of KL is given as 6 cm.

Since JK = KL (from the tick marks), the length of JK is also 6 cm.

In an isosceles triangle, the angles opposite the equal sides are equal.

The side JK is opposite angle L, and the side KL is opposite angle J.

The square symbol at angle K indicates that $\angle K = 90^\circ$ .

The sum of angles in a triangle is $180^\circ$ .

Since $\angle J = \angle L$ and $\angle K = 90^\circ$ , we have $2 \times \angle J + 90^\circ = 180^\circ$ .

Solve for $\angle J$

Therefore, $\angle L = 45^\circ$ .

Observe the tick marks and arrows on quadrilateral ABCD.

Sides AB and DC have single tick marks and arrows, indicating they are equal and parallel.

A quadrilateral with two pairs of opposite sides that are both equal and parallel is a parallelogram.

Identify the side with the same tick mark as AB.

Side AD has a double tick mark and its length is given as 2.5 m.

Side BC also has a double tick mark, indicating it is equal to AD.

Observe the tick marks on quadrilateral EFGH.

In a kite, two pairs of adjacent sides are equal.

From the tick marks, HE = GH.

In a kite, the other pair of adjacent sides are also equal, so EF = FG.

Still stuck on this one?

More Mathematics Questions

Use the triangle above to answer the questions that follow. (a) Is this triangle scalene, isosceles, or equilateral? (b) Name two sides of the triangle that are equal. (c) What is the length of JK? (d) Name two equal angles in this triangle. (e) What is the size of angle J and angle L?

Step-by-step solution

Observe the tick marks on the sides of triangle JKL.

A triangle with two equal sides is an isosceles triangle.

Identify the sides with identical tick marks.

The length of KL is given as 6 cm.

Since JK = KL (from the tick marks), the length of JK is also 6 cm.

In an isosceles triangle, the angles opposite the equal sides are equal.

The side JK is opposite angle L, and the side KL is opposite angle J.

The square symbol at angle K indicates that ∠K=90∘\angle K = 90^\circ∠K=90∘.

The sum of angles in a triangle is 180∘180^\circ180∘.

Since ∠J=∠L\angle J = \angle L∠J=∠L and ∠K=90∘\angle K = 90^\circ∠K=90∘, we have 2×∠J+90∘=180∘2 \times \angle J + 90^\circ = 180^\circ2×∠J+90∘=180∘.

Solve for ∠J\angle J∠J

Therefore, ∠L=45∘\angle L = 45^\circ∠L=45∘.

Observe the tick marks and arrows on quadrilateral ABCD.

Sides AB and DC have single tick marks and arrows, indicating they are equal and parallel.

A quadrilateral with two pairs of opposite sides that are both equal and parallel is a parallelogram.

Identify the side with the same tick mark as AB.

Side AD has a double tick mark and its length is given as 2.5 m.

Side BC also has a double tick mark, indicating it is equal to AD.

Observe the tick marks on quadrilateral EFGH.

In a kite, two pairs of adjacent sides are equal.

From the tick marks, HE = GH.

In a kite, the other pair of adjacent sides are also equal, so EF = FG.

Still stuck on this one?

More Mathematics Questions

The square symbol at angle K indicates that $\angle K = 90^\circ$ .

The sum of angles in a triangle is $180^\circ$ .

Since $\angle J = \angle L$ and $\angle K = 90^\circ$ , we have $2 \times \angle J + 90^\circ = 180^\circ$ .

Solve for $\angle J$

Therefore, $\angle L = 45^\circ$ .