Question

the keypad will have the following symbols. which symbols have symmetry? classify each symbol by listing the letter above it next to the appropriate type of symmetry.
a b c d e f g h i j k l

1. rotational:
2. translational:
3. reflectional:
4. identify two triangles in the diagram that are congruent.
5. which triangle is congruent to △xyz?

for 21-22, use △abc and △cde shown.

1. what is m∠bac?
2. what is m∠cde?
3. find the perimeter.

(diagrams: 19 has a diagram with triangles, 20 has a grid with triangles, 21-22 has a diagram with △abc, △cde and angle 92°, 23 has an isosceles triangle with sides 8x - 1, 4x + 5, 2x + 11)

Explanation:

Problem 23: Find the perimeter.

Step1: Identify triangle type

The triangle has two equal angles (marked by the same angle symbols), so it's isosceles. Thus, the sides opposite the equal angles are equal: \(8x - 1 = 4x + 5\).

Step2: Solve for \(x\)

$$
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$$

Step3: Find side lengths

• First equal side: \(8x - 1 = 8(\frac{3}{2}) - 1 = 12 - 1 = 11\)
• Second equal side: \(4x + 5 = 4(\frac{3}{2}) + 5 = 6 + 5 = 11\)
• Base: \(2x + 11 = 2(\frac{3}{2}) + 11 = 3 + 11 = 14\)

Step4: Calculate perimeter

Perimeter \(= 11 + 11 + 14 = 36\).

Answer:

The perimeter of the triangle is \(\boldsymbol{36}\).