Question

grade 8: week of 9/22, math hw - day 1
directions: show all steps of your thinking and - circle final answers!
problem #1 - unit 1 (mild)
δdef≅δyxz 2) δlmn≅δpqr
ef≅ ____ ∠m≅ ____
problem #2 - unit 1 (mild)
δabc≅δfgh 4) δstu≅δxyz
∠f≅ ____ st≅ ____
problem #3 - unit 1 (mild)
if the triangles qrs and bcd are congruent, what is the corresponding part of sq?
problem #4 - unit 1 (medium)
a. what shape is congruent to shape e?
a
b. name two other congruent shapes.

Explanation:

Step1: Recall congruent - triangle property

In congruent triangles, corresponding sides and angles are equal.

Step2: Solve Problem #1

Since $\triangle DEF\cong\triangle YXZ$, the corresponding side of $\overline{EF}$ is $\overline{XZ}$. Since $\triangle LMN\cong\triangle PQR$, $\angle M\cong\angle Q$.

Step3: Solve Problem #2

Since $\triangle ABC\cong\triangle FGH$, $\angle F\cong\angle A$. Since $\triangle STU\cong\triangle XYZ$, the corresponding side of $\overline{ST}$ is $\overline{XY}$.

Step4: Solve Problem #3

If $\triangle QRS\cong\triangle BCD$, the corresponding side of $\overline{SQ}$ is $\overline{DB}$.

Step5: Solve Problem #4a

By observing the shapes, the shape congruent to shape E is shape A.

Step6: Solve Problem #4b

Two other congruent shapes could be shape D and shape F (answers may vary, as long as the shapes have the same size and shape).

Answer:

1. $\overline{XZ}$, $\angle Q$
2. $\angle A$, $\overline{XY}$
3. $\overline{DB}$
4. a. A

b. D and F