Question

1. which of the combinations of sides and angles is sufficient to prove the triangles congruent? choose all that apply

a. two corresponding sides and the non - included angle.
b. two corresponding angles and the non - included side
c. two corresponding sides and the included angle.
d. two corresponding angles and the included side.

1. identify the vertices of the image under the given transformation. select all that apply;

translation: $(x,y)\to(x + 2,y - 3)$
a. $(-2,-7)$
b. $(5,-10)$
c. $(6,-3)$
d. $(-5,-10)$

Explanation:

Question 32

• Option A: Two corresponding sides and the non - included angle (SSA) is not a valid congruence criterion.
• Option B: Two corresponding angles and the non - included side (AAS) is a valid congruence criterion.
• Option C: Two corresponding sides and the included angle (SAS) is a valid congruence criterion.
• Option D: Two corresponding angles and the included side (ASA) is a valid congruence criterion.

Step1: Apply the translation rule to point \(P\)

For a point \((x,y)\) under the translation \((x,y)\to(x + 2,y-3)\)
When \(x=-3,y = 5\), the new \(x\) - coordinate is \(x'=-3 + 2=-1\), the new \(y\) - coordinate is \(y'=5-3 = 2\)

Step2: Apply the translation rule to point \(Q\)

When \(x = 3,y=3\), the new \(x\) - coordinate is \(x'=3+2 = 5\), the new \(y\) - coordinate is \(y'=3-3=0\)

Step3: Apply the translation rule to point \(R\)

When \(x = 2,y=-5\), the new \(x\) - coordinate is \(x'=2 + 2=4\), the new \(y\) - coordinate is \(y'=-5-3=-8\)

Step4: Apply the translation rule to point \(S\)

When \(x=-4,y=-4\), the new \(x\) - coordinate is \(x'=-4+2=-2\), the new \(y\) - coordinate is \(y'=-4-3=-7\)

Answer:

B. Two corresponding angles and the non - included side, C. Two corresponding sides and the included angle, D. Two corresponding angles and the included side

Question 33

First, find the coordinates of points \(P\), \(Q\), \(R\), \(S\) from the graph.
Assume \(P(-3,5)\), \(Q(3,3)\), \(R(2,- 5)\), \(S(-4,-4)\)