Label sides in right angle triangles worksheet - Free Printable

Let’s go step by step to label each side correctly for the given angle in every triangle.

Remember:
- Hypotenuse is always the longest side — it’s opposite the right angle (the 90° corner).
- Opposite is the side that does NOT touch the marked angle (except at the vertex, but not along the side).
- Adjacent is the side that touches the marked angle AND is NOT the hypotenuse.

We’ll go one triangle at a time.

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Triangle with angle α (top right):

- Right angle is at bottom right → so hypotenuse is the slanted top side.
- Angle α is at bottom left.
- Side opposite α: vertical side on the right.
- Side adjacent to α: horizontal bottom side.
→ So:
Opposite = right vertical side
Adjacent = bottom horizontal side
Hypotenuse = top slanted side

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Triangle with angle b (middle right):

- Right angle is at bottom right → hypotenuse is the slanted top side.
- Angle b is at top right.
- Side opposite b: bottom horizontal side.
- Side adjacent to b: right vertical side.
→ So:
Opposite = bottom side
Adjacent = right side
Hypotenuse = top slanted side

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Triangle with angle c (top left):

- Right angle is at bottom right → hypotenuse is the slanted left side.
- Angle c is at top.
- Side opposite c: bottom horizontal side.
- Side adjacent to c: right vertical side.
→ So:
Opposite = bottom side
Adjacent = right side
Hypotenuse = left slanted side

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Triangle with angle d (middle right, below b):

- Right angle is at top right → hypotenuse is the bottom slanted side.
- Angle d is at bottom left.
- Side opposite d: right vertical side.
- Side adjacent to d: top horizontal side? Wait — no, let’s look again.

Actually, this triangle has right angle at top right. So:

- Hypotenuse = side opposite right angle → that’s the bottom side (longest side).
- Angle d is at bottom left.
- Opposite side to d: the side going up to the right angle → that’s the right-side leg.
- Adjacent side to d: the top side (from angle d to the right angle) — wait, no.

Wait — better way: from angle d, which sides touch it?

Angle d is at bottom left vertex.

Two sides meet there:
1. The bottom side (which is the hypotenuse) — we don’t call this adjacent or opposite; hypotenuse is separate.
2. The left-up side — that’s the other leg.

But actually, in standard labeling:

From angle d:
- Opposite = side not touching d → that’s the right-side leg (vertical-ish).
- Adjacent = side touching d and not hypotenuse → that’s the top-left leg? No.

Wait — let me redraw mentally:

Triangle with vertices:
- Bottom left: angle d
- Top right: right angle
- Third point: somewhere making the shape.

So sides:
- From d to top-right: one leg (let’s say “left” leg)
- From top-right to third point: other leg (“right” leg)
- From d to third point: hypotenuse (bottom side)

Then:
- Opposite to d: the leg that doesn’t touch d → that’s the “right” leg (from top-right to third point)
- Adjacent to d: the leg that touches d and isn’t hypotenuse → that’s the “left” leg (from d to top-right)
- Hypotenuse: the side opposite the right angle → from d to third point (bottom side)

Yes.

→ So:
Opposite = right leg (not touching d)
Adjacent = left leg (touching d, not hypotenuse)
Hypotenuse = bottom side

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Triangle with angle e (bottom left, isosceles):

This is an isosceles triangle split down the middle by a perpendicular line (altitude), creating two right triangles.

Angle e is at the top, inside the left half.

Right angle is at the base, where the altitude meets the base.

So for the left right-triangle:

- Right angle at bottom center.
- Angle e at top.
- Hypotenuse = the left slanted side (one of the equal sides of the big triangle).
- Opposite to e: the bottom half-base (horizontal segment from center to left).
- Adjacent to e: the altitude (vertical line from top to center).

→ So:
Opposite = bottom left half (horizontal)
Adjacent = vertical altitude
Hypotenuse = left slanted side

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Triangle with angle f (bottom right, rectangle diagonal):

This is a rectangle cut by a diagonal, forming two right triangles.

Angle f is at bottom right corner.

Right angle is also at bottom right? Wait — no.

In the rectangle, all corners are right angles. The diagonal goes from top left to bottom right.

So the triangle we’re looking at has:

- Vertices: top left, bottom right, and... actually, the triangle shown is probably the lower-right triangle formed by the diagonal.

Wait — the diagram shows a rectangle with a diagonal from top left to bottom right, and angle f is marked at the bottom right corner, between the diagonal and the bottom side.

And there’s a right angle mark at the top right corner — meaning the triangle being considered is the one with vertices: top left, top right, bottom right? But then angle f would be at bottom right, and right angle at top right.

Actually, looking again: the right angle symbol is at the top right corner of the rectangle. So the triangle includes:

- Top right corner (right angle)
- Bottom right corner (where angle f is)
- And top left corner? Or bottom left?

The diagonal connects top left to bottom right.

So if we take the triangle that has:

- Right angle at top right
- Angle f at bottom right
- Then the third point must be top left? But then the side from top right to bottom right is vertical, from bottom right to top left is diagonal, and from top left to top right is horizontal.

That makes sense.

So triangle vertices: top left, top right, bottom right.

Right angle at top right.

Angle f at bottom right.

Then:

- Hypotenuse = side opposite right angle → that’s the diagonal from top left to bottom right.
- Opposite to angle f: the side not touching f → that’s the top horizontal side (from top left to top right).
- Adjacent to angle f: the side touching f and not hypotenuse → that’s the right vertical side (from top right to bottom right).

→ So:
Opposite = top side
Adjacent = right side
Hypotenuse = diagonal

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Triangle with angle h (bottom left):

Right angle is at bottom right.

Angle h is at bottom left.

So:

- Hypotenuse = side opposite right angle → that’s the top slanted side.
- Opposite to h: the right vertical side (doesn’t touch h).
- Adjacent to h: the bottom horizontal side (touches h, not hypotenuse).

→ So:
Opposite = right side
Adjacent = bottom side
Hypotenuse = top slanted side

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Now, let’s compile all answers clearly.

Final Answer:

For angle α:
Opposite = right vertical side
Adjacent = bottom horizontal side
Hypotenuse = top slanted side

For angle b:
Opposite = bottom horizontal side
Adjacent = right vertical side
Hypotenuse = top slanted side

For angle c:
Opposite = bottom horizontal side
Adjacent = right vertical side
Hypotenuse = left slanted side

For angle d:
Opposite = right leg (side opposite d)
Adjacent = left leg (side adjacent to d, not hypotenuse)
Hypotenuse = bottom side

For angle e:
Opposite = bottom left half (horizontal segment)
Adjacent = vertical altitude
Hypotenuse = left slanted side

For angle f:
Opposite = top horizontal side
Adjacent = right vertical side
Hypotenuse = diagonal

For angle h:
Opposite = right vertical side
Adjacent = bottom horizontal side
Hypotenuse = top slanted side