order ab, bc, and cd from least to greatest.

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Accepted Answer

# Explanation:
## Step1: Find angles in triangles
In $\triangle ABE$ (assuming the triangle with $AB$), since two sides are equal (marked with one tick), the base angles are equal. But we focus on using the triangle - angle - side relationship. In a triangle, the larger the angle, the longer the side opposite it.
For $\triangle BCD$, we know the angle opposite $CD$ is $56^{\circ}$.
For $\triangle ABC$ (assuming the relevant triangle), we need to find angles. Let's first consider the triangle with $AB$ and the equal - side triangle. But more straightforwardly, use the exterior - angle or angle - sum properties. However, using the theorem: In a triangle, if $a,b,c$ are side lengths and $A,B,C$ are the angles opposite to them respectively ($a$ opposite $A$, $b$ opposite $B$, $c$ opposite $C$), then $a < b$ if and only if $A < B$.
Let's assume we have two triangles. For the side $AB$: consider the triangle where it is a side. For the side $BC$: assume we find its related angle. For the side $CD$: its related angle is $56^{\circ}$.
Let's calculate the angles opposite the sides.
In the left - hand triangle (with $AB$), assume it's an isosceles triangle (two sides equal). But using the overall figure:
The angle opposite $AB$: Let's assume we consider the non - isosceles part. Wait, using the theorem: In $\triangle BCD$, the side opposite the $56^{\circ}$ angle is $BC$ (wait no, correction).
Let's use the following:
In a triangle, the side length is related to the measure of the opposite angle.
Let’s assume we have three triangles (mentally). For side $AB$: assume the angle opposite to $AB$ (in its triangle) is $x$. For side $BC$: assume we find its opposite angle.
Wait, a better approach:
Let’s use the fact that in a triangle, if we have two sides $a$ and $b$ and angles $A$ and $B$ opposite to them respectively.
For $AB$: assume in its triangle, the angle opposite $AB$ is $58^{\circ}$ (from the given figure).
For $BC$: assume we consider the triangle where it is a side. Let's calculate its opposite angle. Wait, another way:
Let’s use the exterior - angle and angle - sum. But more simply, using the theorem:
In a triangle, the side opposite a larger angle is longer.
Suppose we have three sides $AB$, $BC$, $CD$.
Let’s assume we consider the angles opposite them.
The angle opposite $AB$ (let's call it $\angle1 = 58^{\circ}$), the angle opposite $BC$ (calculate: in the middle triangle, if we assume some angle relations. Wait, no, use the following:
Let’s assume we have two triangles. For the side $CD$: the angle opposite $CD$ (in its triangle) is $56^{\circ}$. For $AB$: assume the angle opposite $AB$ is $58^{\circ}$. For $BC$:
Let’s assume we have a triangle where $BC$ is a side. Suppose we use the fact that $AB = BE$ (from the double - tick marks). Then, in $\triangle BEC$ (assuming), we can find angles. But a quicker way:
Let’s use the following:
If we consider the three sides $AB$, $BC$, $CD$ and their opposite angles.
The angle opposite $CD$ is $56^{\circ}$, the angle opposite $AB$ is $58^{\circ}$. For $BC$, assume we calculate its opposite angle.
Let’s assume we have a triangle where $BC$ is a side. Suppose we use the angle - sum property. But another approach:
Let’s use the theorem: In $\triangle1$ (with $AB$): angle opposite $AB$ is $58^{\circ}$. In $\triangle2$ (with $CD$): angle opposite $CD$ is $56^{\circ}$. For $BC$, assume we have a triangle where its opposite angle is $180-(58 + 56)=66^{\circ}$ (using a combined - angle approach, assuming a linear - pair or adjacent - triangle angle sum).
Since $56^{\circ}<58^{\circ}<66^{\circ}$
## Step2: Apply angle - side relationship
By the triangle - angle - side relationship (in a triangle, $a$ is the side opposite angle $A$, $b$ is the side opposite angle $B$, $c$ is the side opposite angle $C$, and $a < b$ if $A < B$)
Since the angles opposite $CD$, $AB$, $BC$ (let’s assume the angles are $56^{\circ}$, $58^{\circ}$, $66^{\circ}$ respectively)
We have $CD<AB<BC$

# Answer:
$CD < AB<BC$

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Question

Explanation:

Step1: Find angles in triangles

Answer: