Answer :
To determine which set of side lengths could come from a congruent triangle, let's understand what congruent triangles are. Congruent triangles have all corresponding sides equal in length. This means two triangles are congruent if their sides are all the same.
Looking at the given sets of side lengths:
1. [tex]$10 m, 10 m, 14 m$[/tex]
This set includes two sides that are equal (10 m, 10 m). Although the third side (14 m) is different, this combination of side lengths is typically used in isosceles triangles, where at least two sides are equal.
2. [tex]$10 m, 14 m, 14 m$[/tex]
This set also has two sides that are equal (14 m, 14 m). Similar to the first set, this is a characteristic of isosceles triangles.
3. [tex]$42 m, 42 m, 69 m$[/tex]
In this set, two sides are equal (42 m, 42 m). This again describes an isosceles triangle where two sides have the same length.
4. [tex]$42 m, 69 m, 69 m$[/tex]
Here, the set has two equal sides (69 m, 69 m), indicating an isosceles triangle.
All of these sets of side lengths could form triangles where two sides are the same, which would fit the basic definition of congruent triangles as long as corresponding sides in another triangle also matched these lengths. However, strictly speaking of having all sides equal for congruent triangles, none of these are completely congruent triangles on their own, but they could form congruent pairs with another triangle with the exact same set of sides.
Therefore, the sets mentioned can all be part of congruent triangle pairs with matching sets. It is essential to compare with other triangles to determine congruence fully, but each individual set here represents a viable candidate under typical conditions for congruence discussions.
Looking at the given sets of side lengths:
1. [tex]$10 m, 10 m, 14 m$[/tex]
This set includes two sides that are equal (10 m, 10 m). Although the third side (14 m) is different, this combination of side lengths is typically used in isosceles triangles, where at least two sides are equal.
2. [tex]$10 m, 14 m, 14 m$[/tex]
This set also has two sides that are equal (14 m, 14 m). Similar to the first set, this is a characteristic of isosceles triangles.
3. [tex]$42 m, 42 m, 69 m$[/tex]
In this set, two sides are equal (42 m, 42 m). This again describes an isosceles triangle where two sides have the same length.
4. [tex]$42 m, 69 m, 69 m$[/tex]
Here, the set has two equal sides (69 m, 69 m), indicating an isosceles triangle.
All of these sets of side lengths could form triangles where two sides are the same, which would fit the basic definition of congruent triangles as long as corresponding sides in another triangle also matched these lengths. However, strictly speaking of having all sides equal for congruent triangles, none of these are completely congruent triangles on their own, but they could form congruent pairs with another triangle with the exact same set of sides.
Therefore, the sets mentioned can all be part of congruent triangle pairs with matching sets. It is essential to compare with other triangles to determine congruence fully, but each individual set here represents a viable candidate under typical conditions for congruence discussions.
