Grade 10 · Core Mathematics · Lesson 4 of 11

Properties of Reflection in Plane Geometry

A Grade 10 Core Mathematics CBE lesson from the sub-strand Reflection and Congruence. In it, learners state and apply the three fundamental properties of reflection in plane geometry.

Strand Measurements and GeometrySub-strand Reflection and CongruenceLesson code 10CM-22-L440 minutes · 2 slides

KICD learning outcome (b)

Determine the properties of reflection in different situations.

By the end of this lesson, learners should be able to

State and apply the three fundamental properties of reflection in plane geometry.
Demonstrate reflection properties using paper folding, distance measurement, and angle verification.

Key vocabulary

Equidistant: Situated at an equal distance from a specified reference point or line.; Point $P$ and its reflected image $P^{'}$ are equidistant from mirror line $m$ .
Perpendicular: Intersecting at or forming a right angle of exactly ninety degrees.; Line segment $P P^{'}$ is perpendicular to mirror line $m$ at point $X$ .
Congruent: Having the exact same shape and size in geometric figures.; Polygon $D E F G H$ and its reflected image $D^{'} E^{'} F^{'} G^{'} H^{'}$ are congruent shapes.

Lesson preview

Slide 1 · Geometric Properties of ReflectionModel · 18 min

Figure 1: A triangle and its reflected image appear across a vertical mirror line with measured perpendicular distances.

When an object undergoes reflection in a mirror line, three fundamental geometric properties hold. First, every point on the object and its corresponding image point are equidistant from the mirror line. Second, the line segment connecting any point to its image is perpendicular to the mirror line. Third, the object and its image are congruent, meaning they have the exact same shape and size, although their relative orientation is reversed across the mirror line. Examine Figure 1 to observe how corresponding points are equidistant from the mirror line.

A point and its reflected image are always at equal distances from the mirror line.
The line segment connecting an object point to its image is perpendicular to the mirror line.
Reflected images preserve identical side lengths and angle measures of the original object.
An object and its reflected image are congruent but have opposite spatial orientations.

Worked example. Identify that corresponding points

P

and

P^{'}

are equidistant from mirror line

m

. Set distance from

P^{'}

m

equal to distance from

P

m

, which gives

4.5 cm

. Identify that line segment

P P^{'}

connecting point

P

to its image

P^{'}

is perpendicular to line

m

. The angle between line segment

P P^{'}

and mirror line

m

at intersection point

X

is therefore

90^{\circ}

. Answer: Distance of $P^{'}$ from line $m$ is $4.5 cm$ , and the angle at intersection point $X$ is $90^{\circ}$ ..

Check question: Triangle $X Y Z$ is reflected across mirror line $n$ to give image triangle $X^{'} Y^{'} Z^{'}$ . Point $Y$ is at a perpendicular distance of $6.2 cm$ from line $n$ . The line segment $Y Y^{'}$ intersects line $n$ at point $W$ . What is the distance of image point $Y^{'}$ from line $n$ , and what is the angle formed between segment $Y Y^{'}$ and mirror line $n$ at point $W$ ?

Distance is $6.2 cm$ and angle is $90^{\circ}$
Distance is $12.4 cm$ and angle is $90^{\circ}$
Distance is $3.1 cm$ and angle is $90^{\circ}$
Distance is $6.2 cm$ and angle is $180^{\circ}$

Show answer

Distance is $6.2 cm$ and angle is $90^{\circ}$ . In a reflection, an object point and its corresponding image point are equidistant from the mirror line, so the distance of $Y^{'}$ from $n$ is equal to the distance of $Y$ from $n$ , which is $6.2 cm$ . Additionally, the line segment connecting an object point to its image is always perpendicular to the mirror line, meaning it forms a $90^{\circ}$ angle at the point of intersection $W$ .

Slide 2 · Applying Reflection Properties and Paper FoldingPractice · 22 min

Figure 2: A five-sided polygon and its reflection appear across an inclined mirror line with connected corresponding vertices.

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Both slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 10 lessons in this sub-strand

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Properties of Reflection in Plane Geometry

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 11 lessons in Reflection and Congruence