Triangle STR is congruent to triangle XYZ, TR= 14c - 13, and YZ = 10c - 1, Find c and TR
To find the value of c and TR, we need more information. Specifically, we need to know the lengths of at least one other pair of corresponding sides or the measurements of one pair of corresponding angles in order to set up an equation and solve for the variables.
To find the value of c and TR, we need to use the congruence of Triangle STR and Triangle XYZ, as well as the given values of TR and YZ.
Since the triangles are congruent, we can say that their corresponding sides are equal in length. Therefore, we can write the following equations:
TR = YZ
14c - 13 = 10c - 1
To solve this equation for c, we need to isolate the variable c on one side of the equation. Let's do that step by step:
1. Subtract 10c from both sides of the equation:
14c - 10c - 13 = 10c - 10c - 1
Simplifying the equation:
4c - 13 = -1
2. Add 13 to both sides of the equation:
4c - 13 + 13 = -1 + 13
Simplifying the equation:
4c = 12
3. Divide both sides of the equation by 4:
\( \frac{{4c}}{4} = \frac{12}{4} \)
Simplifying the equation:
c = 3
Therefore, the value of c is 3.
Now, to find the value of TR, substitute the value of c into the equation TR = 14c - 13:
TR = 14(3) - 13
TR = 42 - 13
TR = 29
So, the value of TR is 29.
Since STR ≅ XYZ,
TR ≅ YZ, so
14c-13 = 10c-1
...