Videos > Similar Triangles Corresponding Sides and Angles - Geometry, Mathematics
Similar Triangles Corresponding Sides and Angles - Geometry, Mathematics Video Lecture
FAQs on Similar Triangles Corresponding Sides and Angles - Geometry, Mathematics Video Lecture
| 1. What are similar triangles in geometry? |  |
Similar triangles are triangles that have the same shape but may have different sizes. Their corresponding angles are equal, and the ratio of the lengths of their corresponding sides is constant.
| 2. How can we determine if two triangles are similar? | |
Two triangles are similar if their corresponding angles are congruent and their corresponding sides are in proportion. This means that if we can establish that all three pairs of corresponding angles are equal, then the triangles are similar. Additionally, if the ratio of the lengths of corresponding sides in both triangles is the same, then they are also similar.
| 3. What is the significance of corresponding sides in similar triangles? | |
Corresponding sides in similar triangles are proportional. This means that if we know the ratio of the lengths of two corresponding sides, we can use this ratio to find the lengths of other corresponding sides. It allows us to relate the measurements of different sides in similar triangles.
| 4. How can similar triangles be useful in real-life applications? | |
Similar triangles are widely used in real-life applications, such as in architecture, engineering, and mapmaking. They allow us to determine unknown distances or heights by using measurements from known similar triangles. For example, surveyors can use similar triangles to estimate the heights of buildings or trees without physically measuring them.
| 5. Can we determine if two triangles are similar based on their side lengths alone? | |
No, determining similarity solely based on side lengths is not enough. While having proportional side lengths is a necessary condition for similarity, it is not sufficient. We also need to compare the corresponding angles of the triangles to establish similarity.
Text Transcript from Video
the two triangles shown below are
similar identify their corresponding
sides and angles so we see here based on
how its marked that this angle is equal
to that angle this angle with two arcs
here is equal to this angle with two
arcs here and this angle over here with
three arcs is equal to this angle with
three arcs over there so that's how we
can identify which angles correspond to
which other ones so for example angle
angle c a.b angle c a.b corresponds
corresponds to this angle over here
which we can call which we can call f d
e corresponds to angle f d e if we say
angle ABC angle a b c this corresponds
so now we're looking at this angle right
over here angle ABC corresponds to angle
D e F angle d e f and then finally angle
BCA angle B C a which is that angle over
there corresponds we look at the three
bars corresponds to angle e FD
corresponds to angle e FD now when we
think about corresponding sides and let
me color code it actually that'll make
it a little bit more interesting side a
B so let's say side a B side a B segment
a B I guess you could call it
corresponds to what well you can tell by
looking at the angles this is the side
between this one arc angle and this two
arc angle decide between the one arc
angle and the two arc angle it
corresponds to side de on this triangle
the segment to segment de then if we
look at at BC right over here if we look
at BC right over here
BC corresponds to its between the two
bars and the three bars between the two
bars and the three bars it corresponds
to yeah
EF another way that you could think
about it is that this blue side is
opposite this angle angle e DF so it's
or f de we called it what we called it f
de over here it's opposite an angle and
it's opposite this angle the one arc
angle the one arc angle this orange side
was opposite the 3 arc angle it was
opposite the 3 arc angle and then
finally if we look at this side right
over here AC AC it corresponds to well
it's the only one that's left but it's
also AC is opposite that 2 bar angle
opposite that 2 bar angle is right over
here it corresponds to side DF this
corresponds to side DF on this smaller
triangle right over here and we're done
we've shown all the corresponding sides
and angles
similar identify their corresponding
sides and angles so we see here based on
how its marked that this angle is equal
to that angle this angle with two arcs
here is equal to this angle with two
arcs here and this angle over here with
three arcs is equal to this angle with
three arcs over there so that's how we
can identify which angles correspond to
which other ones so for example angle
angle c a.b angle c a.b corresponds
corresponds to this angle over here
which we can call which we can call f d
e corresponds to angle f d e if we say
angle ABC angle a b c this corresponds
so now we're looking at this angle right
over here angle ABC corresponds to angle
D e F angle d e f and then finally angle
BCA angle B C a which is that angle over
there corresponds we look at the three
bars corresponds to angle e FD
corresponds to angle e FD now when we
think about corresponding sides and let
me color code it actually that'll make
it a little bit more interesting side a
B so let's say side a B side a B segment
a B I guess you could call it
corresponds to what well you can tell by
looking at the angles this is the side
between this one arc angle and this two
arc angle decide between the one arc
angle and the two arc angle it
corresponds to side de on this triangle
the segment to segment de then if we
look at at BC right over here if we look
at BC right over here
BC corresponds to its between the two
bars and the three bars between the two
bars and the three bars it corresponds
to yeah
EF another way that you could think
about it is that this blue side is
opposite this angle angle e DF so it's
or f de we called it what we called it f
de over here it's opposite an angle and
it's opposite this angle the one arc
angle the one arc angle this orange side
was opposite the 3 arc angle it was
opposite the 3 arc angle and then
finally if we look at this side right
over here AC AC it corresponds to well
it's the only one that's left but it's
also AC is opposite that 2 bar angle
opposite that 2 bar angle is right over
here it corresponds to side DF this
corresponds to side DF on this smaller
triangle right over here and we're done
we've shown all the corresponding sides
and angles
About this Video
Sep 10, 2025
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