Bella wants to use transformation to show that GHI is congruent LKJ to illustrate the SSS triangle congruence criterion. Which of the following could she do first
In order to show that two triangles are congruent using the SSS (Side-Side-Side) criterion, Bella could start by showing that their corresponding sides are congruent.
Therefore, Bella could first identify and compare the lengths of the sides in triangle GHI (GH, HI, and GI) with the corresponding sides in triangle LKJ (LK, KJ, and LJ) to check if they are equal.
To use transformation to show that triangle GHI is congruent to triangle LKJ, Bella could start by doing the following:
- Identify a transformation that preserves shape and size. This could be a translation, rotation, or reflection.
- Choose a point on triangle GHI, and apply the chosen transformation to map that point to a corresponding point on triangle LKJ.
- Repeat the process for two more points on triangle GHI, ensuring that the corresponding points on triangle LKJ are also determined by the same transformation.
- Once all three pairs of corresponding points have been identified, Bella can state that triangle GHI is congruent to triangle LKJ by the SSS (Side-Side-Side) congruence criterion.
To show that two triangles are congruent using the Side-Side-Side (SSS) congruence criterion, Bella can use transformations. Here are the steps she can follow:
1. Determine the corresponding sides of the two triangles:
- In this case, Bella needs to identify the sides of triangle GHI that correspond to the sides of triangle LKJ. She can match side GH to side LK, side HI to side KJ, and side GI to side LJ.
2. Apply a translation, rotation, or reflection to align the corresponding sides:
- Bella can start by using a translation to move triangle GHI so that side GH coincides with side LK. She can do this by shifting the entire triangle horizontally or vertically.
3. Apply a rotation or reflection to align the other corresponding sides:
- After aligning side GH with side LK, Bella can apply a rotation or reflection to align side HI with side KJ and side GI with side LJ. She can rotate the triangle around a point, such as the intersection of the corresponding sides, or reflect it across a line.
4. Verify that the corresponding sides have the same lengths:
- Once Bella has aligned the sides using transformations, she can measure the lengths of the corresponding sides (GH with LK, HI with KJ, and GI with LJ) to check if they are equal.
By following these steps, Bella can use transformations to show that triangle GHI is congruent to triangle LKJ using the SSS congruence criterion. Now, back to the question, the first step Bella should do is to determine the corresponding sides of the triangles GHI and LKJ (step 1).