Rectangle Geometry: Is Side BD Perpendicular to DC?

Q: How can I tell if two sides are perpendicular in a rectangle?

Two sides are perpendicular if they meet at a vertex and form a 90° angle. In rectangle ABCD, sides BD and DC meet at point D, so they are perpendicular!

Q: What's the difference between perpendicular sides and diagonals?

Perpendicular sides meet at vertices forming 90° angles. Diagonals (like AC and BD) connect opposite corners but are not perpendicular in rectangles.

Q: Do all rectangles have perpendicular sides?

Yes! By definition, a rectangle has four right angles (90°), which means all adjacent sides are perpendicular to each other.

Q: How do I identify perpendicular lines in the diagram?

Look for the small square symbols at the corners - these mark 90° angles. When two lines meet at a 90° angle, they are perpendicular.

Q: Is side BD actually a side of the rectangle?

Yes! BD is the right side of rectangle ABCD, connecting vertices B and D. It's perpendicular to both the top side (AB) and bottom side (CD).

Rectangle Properties with Perpendicular Sides

Is side BD perpendicular to DC in the rectangle shown below?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is BD perpendicular to CD?

00:03 A perpendicular creates a right angle at the intersection point between the lines

00:06 In a rectangle, all angles are right angles

00:11 There is a right angle between BD and CD, therefore they are perpendicular

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Is side BD perpendicular to DC in the rectangle shown below?

Step-by-step solution

In a rectangle, the sum of all angles equals 90 degrees.

Let's mark all the angles in the rectangle:

Now, let's find the point of intersection between side BD and side DC, drawing a 'T' as follows:

At this point it is clear that the lines do indeed form a 90-degree angle and are, therefore, perpendicular.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: All interior angles in rectangles are exactly 90 degrees
Technique: Look for right angle markers (small squares) at vertices
Check: Adjacent sides always meet at 90° angles forming perpendicular lines ✓

Common Mistakes

Avoid these frequent errors

Confusing which sides are perpendicular
Don't assume diagonal sides like BD and AC are perpendicular = wrong answer! Diagonals in rectangles are equal but not perpendicular. Always check that sides meet at a vertex to form 90° angles.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

FAQ

Everything you need to know about this question

How can I tell if two sides are perpendicular in a rectangle?

Two sides are perpendicular if they meet at a vertex and form a 90° angle. In rectangle ABCD, sides BD and DC meet at point D, so they are perpendicular!

What's the difference between perpendicular sides and diagonals?

Perpendicular sides meet at vertices forming 90° angles. Diagonals (like AC and BD) connect opposite corners but are not perpendicular in rectangles.

Do all rectangles have perpendicular sides?

Yes! By definition, a rectangle has four right angles (90°), which means all adjacent sides are perpendicular to each other.

How do I identify perpendicular lines in the diagram?

Look for the small square symbols at the corners - these mark 90° angles. When two lines meet at a 90° angle, they are perpendicular.

Is side BD actually a side of the rectangle?

Yes! BD is the right side of rectangle ABCD, connecting vertices B and D. It's perpendicular to both the top side (AB) and bottom side (CD).

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