Rectangle Diagonal Segments: Finding Equal Parts to BM = 12.5

Q: Why are all four segments from M equal in a rectangle?

In a rectangle, the diagonals are equal in length and bisect each other. This means they cut each other exactly in half, creating four equal segments from the intersection point M.

Q: If BM = 12.5, what's the length of the whole diagonal?

Since M is the midpoint, the whole diagonal $ AC = AM + MC = 12.5 + 12.5 = 25 $. Both diagonals have length 25.

Q: Does this work for all rectangles or just squares?

This property works for all rectangles, including squares! Any rectangle has equal diagonals that bisect each other, creating four equal segments at their intersection.

Q: How can I remember which segments are equal?

Think of the intersection point M as the center - it's equidistant from all four vertices. So BM = MD = AM = MC always!

Rectangle Diagonal Properties with Intersection Points

The rectangle ABCD is shown below.

DC = 24

BM = 12.5

Which segments are equal to BM?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find all segments equal to BM

00:04 In a rectangle opposite sides are parallel

00:19 In a rectangle all angles are right angles

00:34 In a rectangle diagonals bisect and are equal

00:42 Therefore BM is equal to every diagonal segment

00:50 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

The rectangle ABCD is shown below.

DC = 24

BM = 12.5

Which segments are equal to BM?

Step-by-step solution

It is important to remember that the diagonals in a rectangle intersect and are equal to each other,

therefore:

$BM=MD=AM=MC=12.5$

Final Answer

BM=MD=AM=MC=12.5

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: Diagonals are equal in length and bisect each other
Technique: When diagonals intersect at M, BM = MD = AM = MC
Check: All four diagonal segments equal 12.5 from intersection point ✓

Common Mistakes

Avoid these frequent errors

Thinking only opposite segments are equal
Don't assume BM = MD only because they're on the same diagonal = missing half the answer! This ignores that diagonals bisect each other completely. Always remember all four segments from the intersection point are equal: BM = MD = AM = MC.

Practice Quiz

Test your knowledge with interactive questions

The points A and O are shown in the figure below.

Is it possible to draw a rectangle so that the side AO is its diagonal?

FAQ

Everything you need to know about this question

Why are all four segments from M equal in a rectangle?

In a rectangle, the diagonals are equal in length and bisect each other. This means they cut each other exactly in half, creating four equal segments from the intersection point M.

How is this different from other quadrilaterals?

In parallelograms, diagonals bisect each other but aren't equal. In rectangles, diagonals are both equal AND bisect each other, making all four segments from M equal.

If BM = 12.5, what's the length of the whole diagonal?

Since M is the midpoint, the whole diagonal $AC = AM + MC = 12.5 + 12.5 = 25$ . Both diagonals have length 25.

Does this work for all rectangles or just squares?

This property works for all rectangles, including squares! Any rectangle has equal diagonals that bisect each other, creating four equal segments at their intersection.

How can I remember which segments are equal?

Think of the intersection point M as the center - it's equidistant from all four vertices. So BM = MD = AM = MC always!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles for Ninth Grade questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime