Similar and Congruent Figures Question

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Let

$Delta ABC$ and

$Delta PQR$ be triangles such that

$ang A ~= ang P$ and

$ang B ~= ang Q$ . Assume that

$AB < PQ$ . The following questions will show, using similarity transformations, that if two angles of one triangle are congruent with two angles of another triangle, the triangles are similar.

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

After applying the transformation in the previous question to

$Delta A_2 B_2 C_2$ , the newly transformed triangle is

$Delta A_3B_3C_3$ and point

$A_3$ lies on

$bar{PQ}$ . It may be that point

$C_3$ lies on

$bar{PQ}$ . If not, a reflection over the line

$stackrel{leftrightarrow}{PQ}$ , applied to

$Delta A_3 B_3 C_3$ will ensure that it does. Why is it certain that point

$C_4$ (or

$C_3$ if the transformation is unnecessary) will lie on

$bar{QR} ?$

Congruent angles $ang B$ and $ang Q$ must have congruent arms.
Since a translation and rotation have already been applied, a reflection must transform $C$ to $bar{QR}$ .
For two congruent angles, $ang B$ and $ang Q$ , if the vertices are coincident, then the arms must be coincident.
For two congruent angles, $ang B$ and $ang Q$ , if the initial arms are coincident and both angles are measured in the same direction, then the terminal arms must be coincident.

Question Info

Similar and Congruent Figures Question

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3