Question

triangles lhp and rkb are shown, where △lhp ≅ △rkb.
select all the true congruence statements.
□ ∠lhp ≅ ∠rbk
□ (overline{hl} cong overline{bk})
□ ∠krb ≅ ∠hlp
□ △hpl ≅ △krb
□ (overline{hl} cong overline{kr})
□ △plh ≅ △brk

Explanation:

Step1: Use triangle congruence properties

When \(\triangle LHP\cong\triangle RKB\), corresponding parts are congruent.
For angles, \(\angle LHP\) corresponds to \(\angle RKB\) (not \(\angle RBR\)), \(\angle KRB\) does not correspond to \(\angle HLP\).
For sides, \(\overline{HL}\) corresponds to \(\overline{RK}\) (not \(\overline{BK}\)), \(\overline{HL}\cong\overline{RK}\) (not \(\overline{HL}\cong\overline{KR}\)).
For triangles, \(\triangle HPL\) (which is \(\triangle LHP\)) corresponds to \(\triangle KRB\) as \(\triangle LHP\cong\triangle RKB\) implies \(\triangle HPL\cong\triangle KRB\), and \(\triangle PLH\) (which is \(\triangle LHP\)) corresponds to \(\triangle BRK\) as \(\triangle LHP\cong\triangle RKB\) implies \(\triangle PLH\cong\triangle BRK\).

Answer:

\(\triangle HPL\cong\triangle KRB\), \(\triangle PLH\cong\triangle BRK\)